Question

graph the equation $y = -x^2 - 2x + 8$ on the accompanying set of axes. you must plot 5 points including the roots and the vertex. using the graph, determine the equation of the axis of symmetry.

click to plot points. click points to delete them.

Explanation:

Step1: Find roots (y=0)

Set $-x^2 -2x +8 = 0$, rewrite as $x^2 +2x -8 =0$. Factor: $(x+4)(x-2)=0$. Roots: $x=-4, x=2$. Points: $(-4,0), (2,0)$

Step2: Find vertex x-coordinate

Use $x=-\frac{b}{2a}$ for $ax^2+bx+c$. Here $a=-1, b=-2$, so $x=-\frac{-2}{2(-1)}=-1$

Step3: Find vertex y-coordinate

Substitute $x=-1$ into equation: $y=-(-1)^2 -2(-1)+8 = -1+2+8=9$. Vertex: $(-1,9)$

Step4: Find 2 additional points

Choose $x=0$: $y=-(0)^2-2(0)+8=8$, point $(0,8)$
Choose $x=-2$: $y=-(-2)^2-2(-2)+8=-4+4+8=8$, point $(-2,8)$

Step5: Identify axis of symmetry

Axis of symmetry is vertical line through vertex x-coordinate: $x=-1$

Answer:

Plotted points: $(-4,0), (2,0), (-1,9), (0,8), (-2,8)$
Equation of the axis of symmetry: $x=-1$