Question

Quadratic functions “q” and “w” are graphed on the same coordinate grid. The vertex of the graphed of “q” is 11 units below the vertex of the graph of “w”. Which pair of functions could have been used to create the graphs of “q” and “w”?

A. q(x)= 11x^2 and w(x)= x^2
B. q(x)= x^2 + 11 and w(x)= x^2
C. q(x)= -11x^2 and w(x)= x^2
D. q(x)= x^2-11 and w(x)= x^2

Answer 1

D

Explanation:

Given y = f(x) then the graph of y = f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift of c units up

• If c < 0 then a shift of c units down

Here the graph of q(x) is 11 units below the graph of w(x)

If w(x) = x² then q(x) = x² - 11 → D

Answer 2

D

Explanation:

When moving down the vertex of a quadratic function, you subtract the amount by which you are moving down. This means the last term(one without a variable) in w is 11 greater than the last term in q. Looking at the possible answers, only D has this relationship, meaning it is the answer.