Question

A parabola has an x-intercept (4,0) and vertex (1,-9). What is the equation of this parabola?

a y=-x2+8x-16
b y=x2-6x-8
c y=1/2x2+ 1/2x-10
d y=x2-2x-8

Answer 1

easy way to check is, you are given two points on the curve. (4,0) means when x = 4, y=0 and similarly (1,-9) means when x = 1, y=-9.

Just plug in the value of x and see if you get the said y value.

That will be your function.

Answer 2

do you want the long answer for how to do it if its NOT multiple choice

Answer 3

Yes please, so I know how to figure it out.

Answer 4

ok first you need to know vertex form:
\[y = a(x-h)^{2} +k\]
(h,k) is vertex
in this case: h = 1, k=-9
the other point is : x = 4 , y=0

now plug this in and solve for constant "a"
\[0 = a(4-1)^{2} -9\]
\[9a-9 = 0\]
a = 1
\[y = (x-1)^{2} -9\]
expand it out to get it in standard form
\[y = (x^{2} -2x+1) -9\]
\[y = x^{2} -2x-8\]