If the point (0, 20) is the y-intercept of the parabola with the vertex is (8, -12), What is the equation for this parabola.

Step-by-step explanation:

f(x) = a(x - h)² + k            - vertex form of the equation of the parabola with vertex (h, k)

so the equation of parabola with the vertex (8, -12) is

f(x) = a(x - 8)² - 12  

The point (0, 20) is the y-intercept means if x=0 then f(x)=20

20 = a(0 - 8)² - 12 

20 +12 = 64a - 12 +12

32 = 64a

a = ³²/₆₄ = ¹/₂

Therefore the equation (in vertex form) of parabla is:

                                  f(x) = ¹/₂(x - 8)² - 12  

Rewrite the expression with the fractional exponent as a radical. The denominator of the fraction determines the root, in this case the cube root. The exponent refers only to the part of the expression immediately to the left of the exponent, in this case x, but not the 2.

Step-by-step explanation: