Question

Write the equation of a quadratic function with roots at -4 and -2, and a vertex at (-3, 1).

Write the equation in standard form.

Answer 1

y = -x² - 6x - 8

Explanation:

ax² + bx + c = 0

Root -4: 16a - 4b + c = 0 ...(1)

Root -2: 4a - 2b + c = 0 ...(2)

vertex(-3,1): 9a - 3b + c = 1 ...(3)

(1)-(2): 12a - 2b = 0 6a - b = 0 b = 6a ...(4)

(3)-(2): 5a - b = 1 5a - 6a = 1 a = -1

b = -6

(2): 4*(-1) - 2*(-6) + c = 0 c = -8

Equation: y = -x² - 6x - 8