Question

graph the function $f(x) = -5x^2 - 10x - 4$. plot the vertex. then plot another point on the parabola. if you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first. graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines

Explanation:

Step1: Find vertex x-coordinate

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

Step2: Find vertex y-coordinate

Substitute $x=-1$ into $f(x)$:
$f(-1)=-5(-1)^2 -10(-1) -4 = -5 +10 -4 = 1$

Step3: Find a second point

Choose $x=0$, substitute into $f(x)$:
$f(0)=-5(0)^2 -10(0) -4 = -4$

Answer:

1. Vertex point: $(-1, 1)$
2. Second point: $(0, -4)$

(Plot these two points and draw a downward-opening parabola symmetric about $x=-1$ through them.)