Question

HELP URGENT - put 27 points on question please help!

Write a quadratic function in standard form whose graph passes through (-5,0), (9,0), and (8, -39).

f(x) =

Answer 1

f(x) = 3x² - 12x -135

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