Question

graph the function f(x) = -x² - 4x - 10. 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.

Explanation:

Step1: Find vertex x-coordinate

For $f(x)=ax^2+bx+c$, $x_v = \frac{-b}{2a}$. Here $a=-1, b=-4$:
$x_v = \frac{-(-4)}{2(-1)} = \frac{4}{-2} = -2$

Step2: Find vertex y-coordinate

Substitute $x=-2$ into $f(x)$:
$f(-2) = -(-2)^2 -4(-2) -10 = -4 +8 -10 = -6$

Step3: Find another point

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

Answer:

1. Vertex point: $(-2, -6)$
2. Additional point: $(0, -10)$

(Plot these points, then draw a downward-opening parabola symmetric about the line $x=-2$ through them.)