Answer:
f(x) = x^2 -2x - 8
Explanation:
A quadratic function in factored form (x-a)(x-b) has zeros at (a, 0) and (b, 0). We are given the zeros in the graph are (-2, 0) and (4, 0). Thus, insert that into the factored form equation:
(x - (-2))(x - 4)
(x + 2)(x - 4)
Next, plug in a point from the function into the equation to find if a dilation was applied. Since we currently don’t know what the dilation is, let’s set it to variable d. I’ll be using the point (2, -8)
-8 = d(2 + 2)(2 - 4)
-8 = 4*-2d
-8 = -8d
1 = d
The dilation is 1, so the remaining equation is just (x+2)(x-4). To convert it to standard form, just expand the equation:
x^2 -2x - 8