Question

Ali graphs the function f(x) = –(x + 2)2 – 1 as shown.

On a coordinate plane, a parabola opens up. It goes through (negative 3, 0), has a vertex at (negative 2, negative 1), and goes through (negative 1, 0). A vertical dashed line at (negative 2, 0) is parallel to the y-axis.
Which best describes the error in the graph?

The axis of symmetry should be x = –1.
The axis of symmetry should be x = 2.
The vertex should be a maximum.
The vertex should be (–2, 1)

Answer 1

"The vertex should be a maximum."

Reason: f(x) = −(x + 2)^2 − 1 has a negative leading coefficient, so the parabola opens downward. The vertex at (−2, −1) is the maximum point (not a minimum), and the graph should open down.