Question

Consider f(x)=-(x+7)^2+4. Which of the following are true for f(x)?Check all that apply.

Answer 1

A, D, F

Explanation:

A. True, because
`f(x)=-(x+7)^2+4` represents quadratic function (the greatest power of x is 2)

B. False, because this function is quadratic, so cannot be linear

C. False. The vertex of the parabola is at point (-7,4) (see diagram)

D. True. The axes of symmetry is the line x=-7 that passes through the vertex.

E. False. The y-intercept is at point x=0 and
`y=-(0+7)^2+4=-49+4=-45.`

F. True. The graph has the maximum at vertex, where
`y_(max)=4.`

G. False. The graph of the parabola intersects the x-axis at two points (-9,0) and (-5,0), so x=-9 and x=-5 are two real solutions of the equation f(x)=0.