Question

If you apply the changes below to the quadratio parent function, f(x) = x2

what is the equation of the new function?
• Shift 1 unit right.
• Vertically stretch by a factor of 5.
• Reflect over the x-axis.

Answer 1

`f(x) = -5(x+1)^2`

Explanation:

We are given the following function:

`f(x) = x^2`

Shift 1 unit right.

Shifting a function a units to the right is finding f(x+a). So

To shift one unit right:

`(x+1)^2`

Vertically stretch by a factor of 5.

To vertically stretch by a factor of 5, we multiply the function by 5. So

`5(x+1)^2`

Reflect over the x-axis.

To reflect over the x-axis we multiply the function by -1. So

`f(x) = -5(x+1)^2`