Question

how to find an equation in the form y-k=a(x-h)^2 if the x intercepts are -2 and 6 and the y-intercept is -6?

Answer 1

if you know the two x-intercepts, then you can add them up and divide by 2 to get the value of h

Answer 2

-2+6 = 4/2 = 2
h=2

Answer 3

yep

Answer 4

the y intercept is -6

so x = 0 and y = -6


y-k=a(x-h)^2
y-k=a(x-2)^2 ... plug in h = 2
-6-k=a(0-2)^2 ... plug in (x,y) = (0,-6)
-6-k = a(-2)^2
-6 - k = 4a
-6 - k+6 = 4a+6
-k = 4a + 6
k = -4a - 6



Now let's plug in an x intercept, say (x,y) = (-2,0)


y-k=a(x-2)^2
0-k=a(-2-2)^2
-k = a(-4)^2
-k = 16a
k = -16a
-4a - 6 = -16a ... replace k with -4a-6


now solve for 'a' to get a = ???

Answer 5

a=1/2

Answer 6

yes, a = 1/2

k = -4a - 6
k = -4(1/2) - 6
k = ???

Answer 7

k=-8

is the final equation y+8=(1/2)(x-2)^2?

Answer 8

yes it is

Answer 9

Oh, thank you very much!

Answer 10

you're welcome