graph the equation $y = -x^2 - 10x - 24$ on the accompanying set of axes. you must plot 5 points including…

Explanation:

Step1: Find roots (y=0)

Set $y=0$: $-x^2 -10x -24 = 0$ Multiply by -1: $x^2 +10x +24 = 0$ Factor: $(x+4)(x+6)=0$ Roots: $x=-4, x=-6$ → Points $(-4,0), (-6,0)$

Step2: Find vertex x-coordinate

Use $x=-\frac{b}{2a}$ for $ax^2+bx+c$ $a=-1, b=-10$: $x=-\frac{-10}{2(-1)} = -5$

Step3: Find vertex y-coordinate

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

Step4: Find 2 additional points

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

Answer:

The 5 points to plot are: $(-6, 0)$, $(-5, 1)$, $(-4, 0)$, $(-3, -3)$, $(-7, -3)$