Question

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

Answer 1

8 (answer C)

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)