Question

Use the graph of a translated function below to answer this question: cubic graph going through turning point of (−2, −3) Given the parent function of f(x) = x3, what is the value of h in the translated graph of f(x − h) + k?

Answer 1

`h=-2`

Explanation:

Parent function
`f(x)=x^3`

Translated function
`f(x)=(x-h)^3+k`

Where,

• h is the horizontal translation (x point), and
• k is the vertical translation (y point)

For the original function, the turning point is at (0,0) and for the translated function, (-2,-3) is the turning point. So x point of -2 should be in place of h, and y point of -3 should be in place of k.

Hence, value of h is -2.

Answer 2

To translate x^3 to new function we move it 2 to left to x = -2 then down 3 units to y = -3

New graph is (x - -2)^3 - 3

h = -2