Question

if you apply the changes below to the quadratic parent function, f(x)=x^2, what is the equation of the new function? shifted 1 unit right. vertically streched by a factor of 5. reflected over the x-axis.

Answer 1

f'''(x)=-5(x-1)^2

Explanation:

Given:

f(x)= x^2

Shifting 1 unit to right means subtracting 1 from the function i.e

f(x-1)=(x-1)^2

f'(x)=(x-1)^2

now vertically stretching above f'(x) by a factor of 5:

5f'(x)=5(x-1)^2

f''(x)=5(x-1)^2

finally reflecting above f'''(x) over the x-axis:

-f''(x)=-5(x-1)^2

f'''(x)=-5(x-1)^2 !

Answer 2

`f(x) = - 5 {(x - 1)}^(2)`

Explanation:

The given parent function is:

`f(x) = {x}^(2)`

If we shift to the right by 1 unit, the function becomes:

`f(x) = {(x - 1)}^(2)`

If we stretch by a factor of 5, the function becomes,

`f(x) =5 {(x - 1)}^(2)`

Finally reflecting over the x-axis gives:

`f(x) = - 5 {(x - 1)}^(2)`