+0

# how to find vertex of parabola? It would be simple if there wasnt multiple y's but there is so how i find the vertex what formulas to use

0
394
8

$${\mathtt{X}} = {{\mathtt{Y}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}\left({\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{Y}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{40}}$$

Guest Jun 5, 2015

#1
+26493
+18

This is just a quadratic on its side.  See if the following helps:

.

Alan  Jun 6, 2015
Sort:

#1
+26493
+18

This is just a quadratic on its side.  See if the following helps:

.

Alan  Jun 6, 2015
#2
+91797
+13

Thanks Alan,

X=Y^2-(10Y)+40

This is a sidways parabola. I know because it is the y that is squared.

It opens out in the positive direction. I know that because the coefficient of y^2 is 1 which is POSITIVE.

Now if I can get it into the form

$$(y-k)^2=4a(x-h)$$

then the vertex will be   (h,k)

$$\\X=Y^2-(10Y)+40\\\\ X-40=Y^2-(10Y)\\\\ Y^2-(10Y)=X-40\\\\ Y^2-(10Y)+25=X-40+25\qquad I have completed the square\\\\ (Y-5)^2=X-15\\\\ Vertex is (15,5)$$\$

This the same answer as shown in Alan's graph.   :)

Melody  Jun 6, 2015
#3
+1311
+10

Hi Alan and Melody

When I put this equation in Desmos graph it show the parabola going up instead of side ways like Alan’s graph

It show it going up for all thes equations

X(Y)=Y^2-(10Y)+40

X=Y^2-(10Y)+40

Y=X^2-(10X)+40

it also do it when I leave out the X= part

If I put the colon : in like Alan put in his then it do not work at all. It give an exclamation point!

Can you please show me how to make this work in Desmos graph ?

Dragonlance  Jun 7, 2015
#4
+82944
+8

It seemed to work OK for me,  Dragonlance  .......(???)

Here's the graph.......https://www.desmos.com/calculator/sq4i2l2dtk

CPhill  Jun 7, 2015
#5
+1311
+5

Thank you CPhill

http://web2.0calc.com/questions/desmos-sometimes-not-work-right-if-you-use-capital-letters

to show what the problem was.

Dragonlance  Jun 7, 2015
#6
+26493
+13

Dragonlance wrote: "If I put the colon : in like Alan put in his then it do not work at all..."

I used Mathcad to do that calculation.  In Mathcad (and some other sorts of mathematical software, like Maple, for example)   :=  is used to represent assignment.  This is not the case for all calculational software, and it clearly doesn't work as an assignment operator in Desmos, where a simple  =  is all that is necessary.

Alan  Jun 7, 2015
#7
+1311
+10

Thank you Alan. My TI NSpire use the :=  for some kind of varables.

Does Mathcad treat capital letter VARABLES different than small letter varables ?

Dragonlance  Jun 7, 2015
#8
+26493
+8

Mathcad treats upper and lower case as indicating different variable names, but it doesn't make any assumption about which one should go where on a graph; it leaves that up to the user to decide.

I'd forgotten that the TI_NSpire uses := as well (I have the software-only version, not the physical calculator, and I don't use it very often).

.

Alan  Jun 7, 2015

### 14 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details