Question

The function f(x)=(x-4)(x-2 is shown. What is the range lf the function

Answer 1

Range: y 》-1

Explanation:

f(x) = (x - 2)(x - 4)

f(x) = x² - 2x - 4x + 8

f(x) = x² - 6x + 8

f(x) = x² - 2(x)(3) + 3² - 3² + 8

f(x) = (x - 3)² - 1

Vertex: (3,-1)

Minimum value: -1

Range: y 》-1

Answer 2

The range is all values greater than or equal to -1

y : y≥-1

Explanation:

f(x)=(x-4)(x-2)

This functions is an upwards facing parabola. This means it has a minimum

The minimum is 1/2 way between the zeros

0=(x-4)(x-2)

x-4 =0 x-2 =0

The zeros are at 4 and 2

(4+2)/2 = 6/2 =3

The minimum is at x=3

The minimum value is at

f(3) = (3-4) (3-2) = -1 (1) =-1

The range is all values greater than or equal to -1

y : y≥-1