Question

1. solve the following function by graphing

$-x^2 - 6x - 5 = 0$

Explanation:

Step1: Rewrite as function $y=f(x)$

Let $y = -x^2 -6x -5$

Step2: Find vertex of parabola

Vertex $x$-value: $x=-\frac{b}{2a}=-\frac{-6}{2(-1)}=-3$
Substitute $x=-3$: $y=-(-3)^2-6(-3)-5 = 4$
Vertex: $(-3, 4)$

Step3: Find x-intercepts (set $y=0$)

$$-x^2-6x-5=0 \implies x^2+6x+5=0$$
Factor: $(x+5)(x+1)=0$
Solutions: $x=-5, x=-1$

Step4: Graph key points

Plot vertex $(-3,4)$, intercepts $(-5,0), (-1,0)$, and draw downward-opening parabola; the x-intercepts are the solutions.

Answer:

$x=-5$ and $x=-1$