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.

tickets for the harlem globetrotters

show at michigan state university in

2010 cost $16, $23, or, for vip seats, $40.

total revenue = 16x + 23y + 40z

if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, sales of all three kinds of tickets would

total $46,575.

16x + 23y + 40z = 46575, how many of each kind of ticket would

have been sold?

solve for x, y and z

x − 9z = 0

x − y − z = 55

16x + 23y + 40z = 46575

x = 1170

y = 985

z = 130

welcome!

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right