Question

Which quadratic function fits the three points (1, −2), (2, −2), and (3, −4)?

Answer 1

- x² + 3x -4

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