Suppose the function f (x) = 2x² + kx - 5 is a translation down 13 units and left 2 units of the parent function g (x) = 2x². What is the value of k?

Answer choices

A. k = - 2

B. k = - 13

C. k = 8

D. k = 2

8 (answer C)

Step-by-step explanation:

Start with the parent function g (x) = 2x².

If we graph this, and then translate the whole graph 13 units down, we get

h (x) = 2x² - 13

If we now graph h (x), and translate the entire graph 2 units to the left, the function becomes

h (x) = 2 (x + 2) ^2 - 13, or

h (x) = 2 (x^2 + 4x + 4) - 13, or

h (x) = 2x^2 + 8x + 8 - 13, or

h (x) = 2x^2 + 8x - 5

and if we compare this to

f (x) = 2x^2 + kx - 5

we see readily that k must be 8 (answer C)