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# 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

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

Jun 5, 2015

#1
+27480
+18

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

.

Jun 6, 2015

#1
+27480
+18

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

.

Alan Jun 6, 2015
#2
+97586
+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.   :)

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 Alanâ€™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 ?

Jun 7, 2015
#4
+96302
+8

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

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

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.

Jun 7, 2015
#6
+27480
+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.

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 ?

Jun 7, 2015
#8
+27480
+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).

.

Jun 7, 2015