finding a tangent line to a parabola Unicorn Meta Zoo #1: Why another podcast? ...
I preordered a game on my Xbox while on the home screen of my friend's account. Which of us owns the game?
Why isn't everyone flabbergasted about Bran's "gift"?
How long after the last departure shall the airport stay open for an emergency return?
Additive group of local rings
Implementing 3DES algorithm in Java: is my code secure?
What is the best way to deal with NPC-NPC combat?
Can I criticise the more senior developers around me for not writing clean code?
Does Feeblemind produce an ongoing magical effect that can be dispelled?
Is a 5 watt UHF/VHF handheld considered QRP?
How to use @AuraEnabled base class method in Lightning Component?
Israeli soda type drink
What is the ongoing value of the Kanban board to the developers as opposed to management
How to get even lighting when using flash for group photos near wall?
Arriving in Atlanta after US Preclearance in Dublin. Will I go through TSA security in Atlanta to transfer to a connecting flight?
How to count in linear time worst-case?
How to not starve gigantic beasts
"My boss was furious with me and I have been fired" vs. "My boss was furious with me and I was fired"
Can you stand up from being prone using Skirmisher outside of your turn?
What was Apollo 13's "Little Jolt" after MECO?
What is it called when you ride around on your front wheel?
Putting Ant-Man on house arrest
Why does the Cisco show run command not show the full version, while the show version command does?
Book with legacy programming code on a space ship that the main character hacks to escape
The art of proof summarizing. Are there known rules, or is it a purely common sense matter?
finding a tangent line to a parabola
Unicorn Meta Zoo #1: Why another podcast?
Announcing the arrival of Valued Associate #679: Cesar ManaraHow do I find the equation of a tangent line to a curve?Find intersection(s) between parametrized parabola and a lineHow to find equation of tangent line to $x^2 = 2y$ at $(-3, 9/2)$Find the equation of parabola tangent to a lineWhy is this answer wrong? (point of intersection between parabola and line)Euclid 1999 Question 4(a) - Circle Tangent Intersection4 tangent lines to parabola with points on circleFinding the Equation for the Line Tangent to a Parabola At a Given PointMirror image of the parabola about a tangentMaximizing $x^2 y + y^2 z + z^2 x − x^2 z − y^2 x − z^2 y$ for $x$, $y$, $z$ between $0$ and $1$ (inclusive)Find the numerical value of this expression
$begingroup$
I am practicing for a math contest and I encountered the following problem that I don't know how to solve:
For which value of $b$ is there only one intersection between the line $y = x + b$ and the parabola $y = x^2 + 5x + 3$?
How do I solve it?
algebra-precalculus contest-math
edited 2 hours ago
NoChance
3,79221321
asked 2 hours ago
swagbutton8swagbutton8
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I am practicing for a math contest and I encountered the following problem that I don't know how to solve:
For which value of $b$ is there only one intersection between the line $y = x + b$ and the parabola $y = x^2 + 5x + 3$?
How do I solve it?
algebra-precalculus contest-math
edited 2 hours ago
NoChance
3,79221321
asked 2 hours ago
swagbutton8swagbutton8
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Do you know how to find a derivative?
$endgroup$
– R. Burton
2 hours ago
$begingroup$
Simply $x^2+5x+3=x+b$ must have only one solution, i.e. $x^2+4x+(3-b)=0$ should have zero discriminant.
$endgroup$
– the_fox
2 hours ago
$begingroup$
A Parabola could have many tangent lines...However, it has only 1 min. value, may be this one is the one you are after. More here:desmos.com/calculator/zz7e1nwgf9 and here:info:math.stackexchange.com/questions/92165/…
$endgroup$
– NoChance
2 hours ago
1
$begingroup$
@NoChance Your observation would be relevant if the line’s equation were of the form $y=b$. The line in the problem is not horizontal, though.
$endgroup$
– amd
49 mins ago
$begingroup$
@amd, thanks for your comment. I am not sure which tangent line one should pick then?
$endgroup$
– NoChance
17 mins ago
add a comment |
$begingroup$
I am practicing for a math contest and I encountered the following problem that I don't know how to solve:
For which value of $b$ is there only one intersection between the line $y = x + b$ and the parabola $y = x^2 + 5x + 3$?
How do I solve it?
algebra-precalculus contest-math
edited 2 hours ago
NoChance
3,79221321
asked 2 hours ago
swagbutton8swagbutton8
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I am practicing for a math contest and I encountered the following problem that I don't know how to solve:
For which value of $b$ is there only one intersection between the line $y = x + b$ and the parabola $y = x^2 + 5x + 3$?
How do I solve it?
algebra-precalculus contest-math
algebra-precalculus contest-math
edited 2 hours ago
NoChance
3,79221321
asked 2 hours ago
swagbutton8swagbutton8
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 hours ago
NoChance
3,79221321
asked 2 hours ago
swagbutton8swagbutton8
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 hours ago
NoChance
3,79221321
edited 2 hours ago
NoChance
3,79221321
edited 2 hours ago
NoChance
3,79221321
3,79221321
asked 2 hours ago
swagbutton8swagbutton8
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
swagbutton8swagbutton8
61
asked 2 hours ago
swagbutton8swagbutton8
61
61
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
swagbutton8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Do you know how to find a derivative?
$endgroup$
– R. Burton
2 hours ago
$begingroup$
Simply $x^2+5x+3=x+b$ must have only one solution, i.e. $x^2+4x+(3-b)=0$ should have zero discriminant.
$endgroup$
– the_fox
2 hours ago
$begingroup$
A Parabola could have many tangent lines...However, it has only 1 min. value, may be this one is the one you are after. More here:desmos.com/calculator/zz7e1nwgf9 and here:info:math.stackexchange.com/questions/92165/…
$endgroup$
– NoChance
2 hours ago
1
$begingroup$
@NoChance Your observation would be relevant if the line’s equation were of the form $y=b$. The line in the problem is not horizontal, though.
$endgroup$
– amd
49 mins ago
$begingroup$
@amd, thanks for your comment. I am not sure which tangent line one should pick then?
$endgroup$
– NoChance
17 mins ago
add a comment |
1
$begingroup$
Do you know how to find a derivative?
$endgroup$
– R. Burton
2 hours ago
$begingroup$
Simply $x^2+5x+3=x+b$ must have only one solution, i.e. $x^2+4x+(3-b)=0$ should have zero discriminant.
$endgroup$
– the_fox
2 hours ago
$begingroup$
A Parabola could have many tangent lines...However, it has only 1 min. value, may be this one is the one you are after. More here:desmos.com/calculator/zz7e1nwgf9 and here:info:math.stackexchange.com/questions/92165/…
$endgroup$
– NoChance
2 hours ago
1
$begingroup$
@NoChance Your observation would be relevant if the line’s equation were of the form $y=b$. The line in the problem is not horizontal, though.
$endgroup$
– amd
49 mins ago
$begingroup$
@amd, thanks for your comment. I am not sure which tangent line one should pick then?
$endgroup$
– NoChance
17 mins ago
1
1
$begingroup$
Do you know how to find a derivative?
$endgroup$
– R. Burton
2 hours ago
$begingroup$
Do you know how to find a derivative?
$endgroup$
– R. Burton
2 hours ago
$begingroup$
Simply $x^2+5x+3=x+b$ must have only one solution, i.e. $x^2+4x+(3-b)=0$ should have zero discriminant.
$endgroup$
– the_fox
2 hours ago
$begingroup$
Simply $x^2+5x+3=x+b$ must have only one solution, i.e. $x^2+4x+(3-b)=0$ should have zero discriminant.
$endgroup$
– the_fox
2 hours ago
$begingroup$
A Parabola could have many tangent lines...However, it has only 1 min. value, may be this one is the one you are after. More here:desmos.com/calculator/zz7e1nwgf9 and here:info:math.stackexchange.com/questions/92165/…
$endgroup$
– NoChance
2 hours ago
$begingroup$
A Parabola could have many tangent lines...However, it has only 1 min. value, may be this one is the one you are after. More here:desmos.com/calculator/zz7e1nwgf9 and here:info:math.stackexchange.com/questions/92165/…
$endgroup$
– NoChance
2 hours ago
1
1
$begingroup$
@NoChance Your observation would be relevant if the line’s equation were of the form $y=b$. The line in the problem is not horizontal, though.
$endgroup$
– amd
49 mins ago
$begingroup$
@NoChance Your observation would be relevant if the line’s equation were of the form $y=b$. The line in the problem is not horizontal, though.
$endgroup$
– amd
49 mins ago
$begingroup$
@amd, thanks for your comment. I am not sure which tangent line one should pick then?
$endgroup$
– NoChance
17 mins ago
$begingroup$
@amd, thanks for your comment. I am not sure which tangent line one should pick then?
$endgroup$
– NoChance
17 mins ago
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Hint:
$$x^2+5x+3=x+biff x^2+4x+3-b=0,$$ this quadratic equation should have exactly one solution therefore the discriminant $Delta=?$
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
$endgroup$
add a comment |
$begingroup$
Note that you like the line $y=x+b$ to be tangent to the parabola. The slope of this line is $ m=1.$ Thus the derivative of your parabola should be the same as the slope of the tangent line. Find the point of the tangency and find the $b$ value so that the line passes through that point.
answered 2 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
$endgroup$
add a comment |
$begingroup$
The tangent to parabola has slope $y' = 2x+5$ which should be slope of line =1 at the point of contact. So point of contact is at x=-2. Substituting in parabola,we get y=-3. Now this point lies on line as well.
answered 2 hours ago
TojrahTojrah
5968
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
swagbutton8 is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3201227%2ffinding-a-tangent-line-to-a-parabola%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint:
$$x^2+5x+3=x+biff x^2+4x+3-b=0,$$ this quadratic equation should have exactly one solution therefore the discriminant $Delta=?$
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
$endgroup$
add a comment |
$begingroup$
Hint:
$$x^2+5x+3=x+biff x^2+4x+3-b=0,$$ this quadratic equation should have exactly one solution therefore the discriminant $Delta=?$
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
$endgroup$
add a comment |
$begingroup$
Hint:
$$x^2+5x+3=x+biff x^2+4x+3-b=0,$$ this quadratic equation should have exactly one solution therefore the discriminant $Delta=?$
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
$endgroup$
Hint:
$$x^2+5x+3=x+biff x^2+4x+3-b=0,$$ this quadratic equation should have exactly one solution therefore the discriminant $Delta=?$
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
answered 2 hours ago
HAMIDINE SOUMAREHAMIDINE SOUMARE
3,1471422
3,1471422
add a comment |
add a comment |
$begingroup$
Note that you like the line $y=x+b$ to be tangent to the parabola. The slope of this line is $ m=1.$ Thus the derivative of your parabola should be the same as the slope of the tangent line. Find the point of the tangency and find the $b$ value so that the line passes through that point.
answered 2 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
$endgroup$
add a comment |
$begingroup$
Note that you like the line $y=x+b$ to be tangent to the parabola. The slope of this line is $ m=1.$ Thus the derivative of your parabola should be the same as the slope of the tangent line. Find the point of the tangency and find the $b$ value so that the line passes through that point.
answered 2 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
$endgroup$
add a comment |
$begingroup$
Note that you like the line $y=x+b$ to be tangent to the parabola. The slope of this line is $ m=1.$ Thus the derivative of your parabola should be the same as the slope of the tangent line. Find the point of the tangency and find the $b$ value so that the line passes through that point.
answered 2 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
$endgroup$
Note that you like the line $y=x+b$ to be tangent to the parabola. The slope of this line is $ m=1.$ Thus the derivative of your parabola should be the same as the slope of the tangent line. Find the point of the tangency and find the $b$ value so that the line passes through that point.
answered 2 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
answered 2 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
answered 2 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
answered 2 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
42.2k42061
add a comment |
add a comment |
$begingroup$
The tangent to parabola has slope $y' = 2x+5$ which should be slope of line =1 at the point of contact. So point of contact is at x=-2. Substituting in parabola,we get y=-3. Now this point lies on line as well.
answered 2 hours ago
TojrahTojrah
5968
$endgroup$
add a comment |
$begingroup$
The tangent to parabola has slope $y' = 2x+5$ which should be slope of line =1 at the point of contact. So point of contact is at x=-2. Substituting in parabola,we get y=-3. Now this point lies on line as well.
answered 2 hours ago
TojrahTojrah
5968
$endgroup$
add a comment |
$begingroup$
The tangent to parabola has slope $y' = 2x+5$ which should be slope of line =1 at the point of contact. So point of contact is at x=-2. Substituting in parabola,we get y=-3. Now this point lies on line as well.
answered 2 hours ago
TojrahTojrah
5968
$endgroup$
The tangent to parabola has slope $y' = 2x+5$ which should be slope of line =1 at the point of contact. So point of contact is at x=-2. Substituting in parabola,we get y=-3. Now this point lies on line as well.
answered 2 hours ago
TojrahTojrah
5968
answered 2 hours ago
TojrahTojrah
5968
answered 2 hours ago
TojrahTojrah
5968
answered 2 hours ago
TojrahTojrah
5968
5968
add a comment |
add a comment |
swagbutton8 is a new contributor. Be nice, and check out our Code of Conduct.
swagbutton8 is a new contributor. Be nice, and check out our Code of Conduct.
swagbutton8 is a new contributor. Be nice, and check out our Code of Conduct.
swagbutton8 is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3201227%2ffinding-a-tangent-line-to-a-parabola%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
Do you know how to find a derivative?
$endgroup$
– R. Burton
2 hours ago
$begingroup$
Simply $x^2+5x+3=x+b$ must have only one solution, i.e. $x^2+4x+(3-b)=0$ should have zero discriminant.
$endgroup$
– the_fox
2 hours ago
$begingroup$
A Parabola could have many tangent lines...However, it has only 1 min. value, may be this one is the one you are after. More here:desmos.com/calculator/zz7e1nwgf9 and here:info:math.stackexchange.com/questions/92165/…
$endgroup$
– NoChance
2 hours ago
1
$begingroup$
@NoChance Your observation would be relevant if the line’s equation were of the form $y=b$. The line in the problem is not horizontal, though.
$endgroup$
– amd
49 mins ago
$begingroup$
@amd, thanks for your comment. I am not sure which tangent line one should pick then?
$endgroup$
– NoChance
17 mins ago