type the correct answer in each box. use numerals instead of words. what is the equation of the quadratic…

Explanation:

Step1: Identify x - intercepts

The x - intercepts of the quadratic function are the points where the graph crosses the x - axis. From the graph, the x - intercepts are (x=-2) and (x = 2).

Step2: Write the factored form of the quadratic function

The factored form of a quadratic function is (y=a(x - r_1)(x - r_2)), where (r_1) and (r_2) are the x - intercepts. Here, (r_1=-2) and (r_2 = 2), so the function is (y=a(x + 2)(x - 2)).

Step3: Find the value of (a)

The graph passes through the point ((0,8)). Substitute (x = 0) and (y=8) into (y=a(x + 2)(x - 2)): [ \begin{align*} 8&=a(0 + 2)(0 - 2)\ 8&=a(2)(-2)\ 8&=-4a\ a&=- 2 \end{align*} ]

Answer:

(f(x)=-2(x + 2)(x - 2))