Answer:
f(x) = 3x² - 12x -135
Step-by-step explanation:
standard form of a quadratic equation is
y = Ax² + Bx + C
You are given 3 solutions for X and Y, i.e( x=-5, y = 0), (x = 9,y = 0) and (x = 8,y = -39)
Substitute each of this equations into the quadratic equation to obtain a system of 3 equations
For ( x=-5, y = 0), 25A - 5B + C = 0 ---------- eq (1)
For ( x= 9, y = 0), 81A + 9B + C = 0 ---------- eq (2)
For ( x= 8, y = -39), 64A + 8B + C = -39 ---------- eq (3)
You have 3 equations and 3 unknowns. Solving this system of 3 equations will give:
A = 3, B = -12, c = -135
Hence the quadratic equation is
y = 3x² - 12x -135
or in function form:
f(x) = 3x² - 12x -135
