Question

Consider the graph that represents the following quadratic equation.

Answer 1

Answer:

Part 1) The graphs open downward

Part 2) The vertex is the point (-2,5)

Part 3) The axis of symmetry is x=-2

Step-by-step explanation:

step 1

we have

$y=-\frac{1}{3}(x+2)^2+5$

This is a vertical parabola open downward (because the leading coefficient is negative)

The vertex is a maximum

step 2

The quadratic equation is written in vertex form

$y=a(x-h)^2+k$

where

(h,k) is the vertex

so

In this problem

The vertex is the point (-2,5)

step 3

The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

The x-coordinate of the vertex is -2

therefore

The axis of symmetry is x=-2