Question

Graph the parabola.y = - (x + 2)²- 5Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex.

Answer 1

Solution

We want to graph the parabola

$y=-(x+2)^2-5$

To find the vertex, We will equate

$\begin{gathered} x+2=0 \\ x=-2 \\ \text{and} \\ y=-5 \end{gathered}$

Coordinate of the vertex is (-2, -5)

To the left of the vertex, let us pick x = -3 and x = -5

when x = -3

$\begin{gathered} y=-(x+2)^2-5 \\ y=-(-3+2)^2-5 \\ y=-(-1)^2-5 \\ y=-1-5=-6 \end{gathered}$

Coordinate is (-3, -6)

When x = -5

$\begin{gathered} y=-(x+2)^2-5 \\ y=-(-5+2)^2-5 \\ y=-(-3)^2-5 \\ y=-9-5=-14 \end{gathered}$

Coordinate is (-5, -14)

To the right of the vertex

We can pick x = 0 and x = 1

W