Question

use the parabola tool to graph the quadratic function ( f(x) = x^2 + 10x + 16 ).
graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Explanation:

Step1: Find vertex x-coordinate

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

Step2: Find vertex y-coordinate

Substitute $x=-5$ into $f(x)$:
$f(-5)=(-5)^2+10(-5)+16=25-50+16=-9$
Vertex is $(-5, -9)$

Step3: Find a second point

Choose $x=0$, substitute into $f(x)$:
$f(0)=0^2+10(0)+16=16$
Second point is $(0, 16)$

Step4: Graph using points

Plot vertex $(-5,-9)$ and $(0,16)$, then reflect $(0,16)$ over axis of symmetry $x=-5$ to get $(-10,16)$ for symmetry, then draw the parabola.

Answer:

Vertex: $(-5, -9)$; Second point: $(0, 16)$ (the parabola opens upward, passing through these points and their symmetric counterparts)