Question

The function h(x)=1/2(x+3)^2+2. How is the graph of h(x) translated from the parent graph of a quadratic function, f(x)=x^2? SELECT ALL THAT APPLY.

A. The graph of h(x) is shifted 3 units to the right of the parent graph.

B. The graph of h(x) is shifted 2 units up from the parent graph.

C. The graph of h(x) is vertically compressed by a factor of 1/2

D. The graph of h(x) is a reflection of the parent graph.

E. The graph of h(x) has a different y-intercept from the parent graph.

F. Both graphs have two x intercepts.

Answer 1

B. The graph of h(x) is shifted 2 units up from the parent graph; C. The graph of h(x) is vertically compressed by a factor of 1/2 ; E. The graph of h(x) has a different y-intercept from the parent graph.

Explanation:

Adding 3 to the variable x before the exponent is applied shifts the graph horizontally. Since it is added, this means it is shifted 3 units to the left, not the right.

Adding 2 to the end of the function shifts the graph vertically. Since it is added, it is shifted 2 units up.

Multiplying the function by 1/2 compresses it vertically by a factor of 1/2.

These graphs are not reflections, and neither graph has two x-intercepts.

The two graphs do have different y-intercepts.

Answer 2

The Answers are B,C, and E

I got this by graphing the function of h(x) and the parent function f(x) on the same graph and analogizing the shifts of h(x) from the parent graph f(x). Also the function included two different y-intercepts.