Answer:
- x² + 3x -4
Step-by-step explanation:
From (1, -2) (2, -2)
f(1) = f(2) = -2 ... solve the vertical axis coordinate
x = 1 + ( 2 - 1) = 1.5 ... middle point of 1 and 2
for other points on the function (p, q)
f(x) = p * ( x - 1.5)² + q
for (3, -4)
f(3) = p * (3 - 1.5)² + q = 2.25 p + q = - 4 ...(1)
for (1, -2)
f(1) = p * (1 - 1.5)² + q = 0.25 p + q = - 2 ...(2)
(1) - (2) 2p = -2 p = - 1
q = -2 - 0.25 * (-1) = - 1.75
equation: f(x) = -(x - 1.5)² - 1.75 = - x² + 3x -4
check point(2,-2) f(2) = - (2 - 1.5)² - 1.75 = - 0.25 - 1.75 = - 2
