What is true about the function h(x) = x2 + 20x – 17? Check all that apply. The vertex of h is (–10, –117).The vertex form of the function is h(x) = (x + 20)2 – 17.The maximum value of the function is –17. To graph the function h, shift the graph of f(x) = x2 left 10 units and down 117 units.The axis of symmetry of function h is x = 20.
Answer
A
The vertex of h is (–10, –117).
B
The vertex form of the function is h(x) = (x + 20)2 – 17.
C
The maximum value of the function is –17.
D
To graph the function h, shift the graph of f(x) = x2 left 10 units and down 117 units.
E
The axis of symmetry of function h is x = 20.
Explanation
Complete the square: h(x) = x² + 20x − 17 = (x + 10)² − 117. This gives the vertex (−10, −117), so A is true. Since y = x² is shifted left 10 units and down 117 units to make h, D is also true. The parabola opens upward, so it has a minimum, not a maximum, and its axis of symmetry is x = −10.
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