Solving Quadratic Equations: Quadratic Formula — Unit test
Question 3 • FL-1200700-Mathematics for College Algebra MIS
Which statements are true about the graph of the function h(x) = –5x2 + 60x – 200? Select three options.The axis of symmetry is the line x = –6.The graph of h(x) will not intersect the graph of the parent function, f(x) = x2.The vertex of the graph is at (6, –20).The parabola has a maximum.The value of k, when the equation is written in vertex form, is –200.
Answer
A
The axis of symmetry is the line x = –6.
B
The graph of h(x) will not intersect the graph of the parent function, f(x) = x2.
C
The vertex of the graph is at (6, –20).
D
The parabola has a maximum.
E
The value of k, when the equation is written in vertex form, is –200.
Explanation
The vertex’s x-coordinate is −b/(2a) = −60/(2·−5) = 6, and h(6) = −20, so the vertex is (6, −20) and the axis of symmetry is x = 6, not x = −6. Since the coefficient of x² is negative, the parabola opens downward and has a maximum. In vertex form, h(x) = −5(x − 6)² − 20; setting this equal to the parent function x² gives an equation with no real solutions, so the graphs do not intersect.
AI-written and checked against the verified answer.