Graph of polynomial problem from Gelfands Functions and Graphs
$begingroup$
Working through Gelfands Functions and Graphs but I'm stuck on a question. The question involves an image of a graph of $x^2 + px + q$ from the graph alone you need to find $p$ and $q$.
As you can see from the image below the vertex of the parabola is not known. I can find equations of graphs of parabolas with known vertex co-ordinates but is there any hints to find the equation of this graph?
graphing-functions
edited Dec 22 '18 at 15:37
N. F. Taussig
45.4k103358
asked Dec 22 '18 at 15:28
esc1234esc1234
83
$endgroup$
add a comment |
$begingroup$
Working through Gelfands Functions and Graphs but I'm stuck on a question. The question involves an image of a graph of $x^2 + px + q$ from the graph alone you need to find $p$ and $q$.
As you can see from the image below the vertex of the parabola is not known. I can find equations of graphs of parabolas with known vertex co-ordinates but is there any hints to find the equation of this graph?
graphing-functions
edited Dec 22 '18 at 15:37
N. F. Taussig
45.4k103358
asked Dec 22 '18 at 15:28
esc1234esc1234
83
$endgroup$
1
$begingroup$
You have two points on the graph: $ (4,0)$ and $(5,-3)$ and you know the equation of the parabola is $y=x^2+px+q$. That gives you two simultaneous equations in $p$ and $q$. Can you take it from there?
$endgroup$
– postmortes
Dec 22 '18 at 15:37
1
$begingroup$
thanks very much. I had one of those 'doh!' moments when I read your comment thinking why didn't I think of that. Got the answer now. Thanks!
$endgroup$
– esc1234
Dec 23 '18 at 22:07
add a comment |
$begingroup$
Working through Gelfands Functions and Graphs but I'm stuck on a question. The question involves an image of a graph of $x^2 + px + q$ from the graph alone you need to find $p$ and $q$.
As you can see from the image below the vertex of the parabola is not known. I can find equations of graphs of parabolas with known vertex co-ordinates but is there any hints to find the equation of this graph?
graphing-functions
edited Dec 22 '18 at 15:37
N. F. Taussig
45.4k103358
asked Dec 22 '18 at 15:28
esc1234esc1234
83
$endgroup$
Working through Gelfands Functions and Graphs but I'm stuck on a question. The question involves an image of a graph of $x^2 + px + q$ from the graph alone you need to find $p$ and $q$.
As you can see from the image below the vertex of the parabola is not known. I can find equations of graphs of parabolas with known vertex co-ordinates but is there any hints to find the equation of this graph?
graphing-functions
graphing-functions
edited Dec 22 '18 at 15:37
N. F. Taussig
45.4k103358
asked Dec 22 '18 at 15:28
esc1234esc1234
83
edited Dec 22 '18 at 15:37
N. F. Taussig
45.4k103358
asked Dec 22 '18 at 15:28
esc1234esc1234
83
edited Dec 22 '18 at 15:37
N. F. Taussig
45.4k103358
edited Dec 22 '18 at 15:37
N. F. Taussig
45.4k103358
edited Dec 22 '18 at 15:37
N. F. Taussig
45.4k103358
45.4k103358
asked Dec 22 '18 at 15:28
esc1234esc1234
83
asked Dec 22 '18 at 15:28
esc1234esc1234
83
asked Dec 22 '18 at 15:28
esc1234esc1234
83
83
1
$begingroup$
You have two points on the graph: $ (4,0)$ and $(5,-3)$ and you know the equation of the parabola is $y=x^2+px+q$. That gives you two simultaneous equations in $p$ and $q$. Can you take it from there?
$endgroup$
– postmortes
Dec 22 '18 at 15:37
1
$begingroup$
thanks very much. I had one of those 'doh!' moments when I read your comment thinking why didn't I think of that. Got the answer now. Thanks!
$endgroup$
– esc1234
Dec 23 '18 at 22:07
add a comment |
1
$begingroup$
You have two points on the graph: $ (4,0)$ and $(5,-3)$ and you know the equation of the parabola is $y=x^2+px+q$. That gives you two simultaneous equations in $p$ and $q$. Can you take it from there?
$endgroup$
– postmortes
Dec 22 '18 at 15:37
1
$begingroup$
thanks very much. I had one of those 'doh!' moments when I read your comment thinking why didn't I think of that. Got the answer now. Thanks!
$endgroup$
– esc1234
Dec 23 '18 at 22:07
1
1
$begingroup$
You have two points on the graph: $ (4,0)$ and $(5,-3)$ and you know the equation of the parabola is $y=x^2+px+q$. That gives you two simultaneous equations in $p$ and $q$. Can you take it from there?
$endgroup$
– postmortes
Dec 22 '18 at 15:37
$begingroup$
You have two points on the graph: $ (4,0)$ and $(5,-3)$ and you know the equation of the parabola is $y=x^2+px+q$. That gives you two simultaneous equations in $p$ and $q$. Can you take it from there?
$endgroup$
– postmortes
Dec 22 '18 at 15:37
1
1
$begingroup$
thanks very much. I had one of those 'doh!' moments when I read your comment thinking why didn't I think of that. Got the answer now. Thanks!
$endgroup$
– esc1234
Dec 23 '18 at 22:07
$begingroup$
thanks very much. I had one of those 'doh!' moments when I read your comment thinking why didn't I think of that. Got the answer now. Thanks!
$endgroup$
– esc1234
Dec 23 '18 at 22:07
add a comment |
0
active
oldest
votes
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
});
}
});
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%2f3049547%2fgraph-of-polynomial-problem-from-gelfands-functions-and-graphs%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3049547%2fgraph-of-polynomial-problem-from-gelfands-functions-and-graphs%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
$begingroup$
You have two points on the graph: $ (4,0)$ and $(5,-3)$ and you know the equation of the parabola is $y=x^2+px+q$. That gives you two simultaneous equations in $p$ and $q$. Can you take it from there?
$endgroup$
– postmortes
Dec 22 '18 at 15:37
1
$begingroup$
thanks very much. I had one of those 'doh!' moments when I read your comment thinking why didn't I think of that. Got the answer now. Thanks!
$endgroup$
– esc1234
Dec 23 '18 at 22:07