Question

graph the equation $y = -x^2 - 10x - 24$ 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 $y=0$: $-x^2 -10x -24=0$ → $x^2 +10x +24=0$. Factor: $(x+4)(x+6)=0$. Roots: $x=-4, x=-6$. Points: $(-6,0), (-4,0)$

Step2: Find vertex x-coordinate

Use $x=-\frac{b}{2a}$. For $y=-x^2-10x-24$, $a=-1, b=-10$. $x=-\frac{-10}{2(-1)}=-5$

Step3: Find vertex y-coordinate

Substitute $x=-5$: $y=-(-5)^2 -10(-5)-24=-25+50-24=1$. Vertex: $(-5,1)$

Step4: Find 2 additional points

Choose $x=-3$: $y=-(-3)^2-10(-3)-24=-9+30-24=-3$ → $(-3,-3)$
Choose $x=-7$: $y=-(-7)^2-10(-7)-24=-49+70-24=-3$ → $(-7,-3)$

Step5: Determine axis of symmetry

Axis of symmetry is vertical line through vertex: $x=-5$

Answer:

5 Points to Plot:

$(-7, -3)$, $(-6, 0)$, $(-5, 1)$, $(-4, 0)$, $(-3, -3)$

Equation of Axis of Symmetry:

$x=-5$