Question

Find the quadratic function y=a(x-h)^2 whose graph passes through the given points. (12,-7) and (9,0)

Answer 1

Answer:

y = (-7/3)(x - 9)

Step-by-step explanation:

(12, - 7)

y = a(x - h)^2

-7 = a(12 - h)^2

- 7 = a(144 - 24x + h^2)

(9,0)

0 = a(x - h)^2

0 = a(9 - h)^2

0 = a(81 - 18h + h^2)

From (9,0) we can conclude that

a = 0

or

(9 - h)^2 = 0

Let's try the second possibility.

Take the square root of both sides.

9 - h = sqrt(0)

Add h to both sides

9 - h = 0  

h = 9

So now what we have is

y = a(x - 9)

Use the first equation to get a

-7 = a(12 - 9)

-7 = a(3)

-7/3 = a

Answer

y = (-7/3)(x - 9)