Question

The vertex of the parabola below is at the point
(3, 6), and the point (4, 4) is on the parabola. What is the equation of the parabola?



A. y = -2(x - 3)^2 + 6
B. x = 2(y - 3)^2 + 6
C. y = -4(x - 3)^2 + 6
D. y = -2(x - 6)^2 + 3

Answer 1

The vertex form of a parabola is written as

\[y = a(x - h)^2 + k\]

the vertex is (x,h)

so plug in your vertex numbers in for 'h' and for 'k'

now you'll have

\[y = a(x - 3)^2 + 6\]

now you take your point you have (4,4) and plug that in for 'x' and for 'y'

\[4 = a(4 - 3)^2 + 6\]

You want to solve for 'a' here....what does 'a' equal ...?

Answer 2

a=2?

Answer 3

Close...-2

4 - 3 = 1
1^2 = 1

a + 6 = 4
a = -2

so Now that is your 'a' ...what is your equation?

Answer 4

A. y = -2(x - 3)^2 + 6

Answer 5

Perfect!

Answer 6

sweet!