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.

D.

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

Standard form:   f(x) = 2/3x^2 + 4x.

Step-by-step 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.

the battle of gettysburg is considered the "high water mark" of the confederacy because it marked the greatest advance of the confederate forces against the union.

step-by-step explanation: given equation a = h(b 1+b 2)

also we are given values of a, h and b 1 as :

a = 16, h = 4, and b 1 = 3.

in order to solve it for b 2, we need to plug the given values of   a, h and b 1 .

therefore, plugging values of   a, h and b 1   in given equation, we get

16 = 4( 3 + b 2)

first dividing both sides by 4, we get

4 = 3 + b 2

subtracting 3 from both sides, we get

4 -3 = 3 -3 + b 2

1 = b 2.