Question

Choose the function that shows the correct transformation of the quadratic function shifted eight units to the left and one unit down.

ƒ(x) = (x - 8)2 - 1
ƒ(x) = (x - 8)2 + 1
ƒ(x) = (x + 8)2 - 1
ƒ(x) = (x + 8)2 + 1

Answer 1

ƒ(x) = (x - 8)² - 1

Explanation:

Start with the basic function: f(x) = x².

To shift the parabola eight units to the left, you must add eight units to the value of x. The equation for the parabola becomes

ƒ(x) = (x - 8)².

To shift the parabola down one unit, you subtract one unit from the function. The equation becomes

ƒ(x) = (x -8)² - 1.

The figure below shows the graphs of ƒ(x) = x² (red), ƒ(x) = (x - 8)² (blue), and ƒ(x) = (x - 8)² - 1 (green).