The function f(x) = –3x2 + 36x – 119 written in vertex form is f(x) = –3(x – 6)2 – 11. which statements are true about the graph of f(x)? check all that apply.

the axis of symmetry is the line x = 6.

the vertex of the graph is at (–6, –11).

the parabola has a minimum.

the parabola opens down.

the value of h, when the equation is written in vertex form, is positive.

Analysis:

f(x) = –3(x – 6)^2 – 11

means vertex is at x = 6 and y = - 11

The negative sign in front of x^2 means the parabola opens downward.

The, the vertex is a maximum point, which is below the x-axis (because it is negative). Therefore the parabola do not cross the x-axis, meaning that all the y-values are negative (≤ -11).

Options:

The axis of symmetry is the line x = 6.---> true, the symetry line is vertical and passes through the vertex

The vertex of the graph is at (–6, –11).---> false, it is (6, -11)

The parabola has a minimum.---> false, y values have not a lower bound.

The parabola opens down.---> true, because the negative sign in front ox x^2

The value of h, when the equation is written in vertex form, is positive. ---> false, the value of h is positive. It is 6. Although h is preceeded by a  negative sign in the equation, h itself is positive.