Question

Find the range of the function.

f(x) = (x - 2)^2 + 2

Answer 1

All real numbers
y ≥ 0
y > 2
y ≥ 2 this one ?

Answer 2

1. Expand the expression on the right side until we get a quadratic expression:
f(x) = (x - 2)^2 + 2
= (x - 2)(x - 2) + 2
= x(x - 2) -2(x - 2) + 2
= x^2 - 4x - 4x + 4 + 2
= x^2 - 8x + 6


We know the graph opens upward, so next find the vertex using x = -b/(2a):

x = -(-8)/2(1) = 8/2 = 4

y = (4)^2 -8(4) + 6
= 16 - 32 + 6
= -(32 -16 - 6)
= -(32 - 22)
= -10

So the vertex of the parabola is (4, -10)

This means that vertically, the parabola begins at y = -10, and extends upward. Therefore, the range of the function is (-10, ∞)

Answer 3

@lornbeach