 # Writing quadratic equations from a parabola's coordinates

I’m year 11 and doing a old Maths paper at the moment and I’ve come to the exellence question.

I have a parabola that has the following co ordinates and i am in desperate need on how to make them in to a quadratic equation

(5, 0)
(25,0)
(15,10) thats the maximum

there’s no Y intersept as the graph doessn’t show it

the answer sheet gives the equation:

y = -0.1(x-15)^2+10

any help on how they got that would be much appreciated

Hi GeoNerd

Welcome to the Studyit forum.

If we draw the graph of the equation they give as an answer we find that it goes through the two points on the x axis (5,0) and (25,0). Not the two points on the y axis you give.

1…y = x2

The question tells us that the maximum is (15,10).
This tells us that the vertex 0 (which was at (0,0), has been moved 15 across and 10 up.
We have to adjust the equation by replacing y with (y-10) and x with (x-15).

2…y-10 = (x-15)^2

The parabola may have been stretched in someway. We need a coefficient to show this.

3…y-10 = a(x-15)2

If this parabola goes through the point (5,0), then we can substitute those coordinates in the equation to find the value of a.

4…0-10 = a(5-15)2
5…-10 = a.102
6…a = -0.1

So the equation is

7…y = -0.1(x-15)2 + 10

Cheers
MT