Solve the following equations in the forms asked.

Below in bold.

Step-by-step explanation:

Vertex form.

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

The point (h, k) is the vertex so from the graph:

y = a(x - 1)^2 - 8

From the x -interesect we see that x = 6 when y = 0 so

0 = a(6 - 1)^2 - 8

25a - 8 = 0

a = 8/25

So the vertex form is

y = (8/25)(x - 1)^2 - 8.

Factored form:

y = (8/25)(x + 4)(x - 6)  

- as -4 and 6 are the zeros of the equation.

Standard form:

From the factored form we have

y = (8/25)(x^2 - 2x - 24)

y = 8/25 x^2 - 16/25 x - 192/25

or (in decimal form):

y = 0.32x^2 - 0.64x - 7.68.