Question

Find the equation, f(x) = a(x-h)2 + k, for a parabola that passes through the point (0, 0) and has (-3, -6) as its vertex. What is the standard form of the equation?

A) The vertex form of the equation is f(x) = −2/3(x + 3)^2 - 6. The standard form of the equation is f(x) =2/3x^2 + 4x.
B) The vertex form of the equation is f(x) =2/3(x + 3)^2 - 6. The standard form of the equation is f(x) = −2/3x^2 - 4x.
C) The vertex form of the equation is f(x) =−2/3(x - 3)^2 - 6. The standard form of the equation is f(x) =2/3x^2 - 4x.
D) The vertex form of the equation is f(x) =2/3(x + 3)^2 - 6. The standard form of the equation is f(x) =2/3x^2 + 4x.

Answer 1

D.

Vertex form: f(x) = 2/3(x + 3)^2 - 6.

Standard form: f(x) = 2/3x^2 + 4x.

Explanation:

The vertex is at (-3, -6) so the vertex form is

y = a(x - (-3))^2 - 6

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

Now we find the value of a by substituting x = 0 and y = 0:

0 = a(0 + 3)^2 - 6

9a = 6

a = 2/3.

Vertex form is y = 2/3(x + 3)^2 - 6.

Convert to Standard form:

Multiply through by 3:

3y = 2(x + 3)^2 - 18

3y = 2x^2 + 12x + 18 - 18

3y = 2x^2 + 12x

y = 2/3x^2 + 4x.