Question

graph the parabola.
$y = x^2 + 10x + 21$
plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. then click on the graph - a - function button.

Explanation:

Step1: Find vertex x-coordinate

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

Step2: Find vertex y-coordinate

Substitute $x=-5$ into the equation:
$y=(-5)^2 + 10(-5) + 21 = 25 - 50 + 21 = -4$
Vertex: $(-5, -4)$

Step3: Pick left x-values, find y

Choose $x=-7, x=-6$:
For $x=-7$: $y=(-7)^2 +10(-7)+21=49-70+21=0$
For $x=-6$: $y=(-6)^2 +10(-6)+21=36-60+21=-3$
Left points: $(-7,0), (-6,-3)$

Step4: Pick right x-values, find y

Choose $x=-4, x=-3$:
For $x=-4$: $y=(-4)^2 +10(-4)+21=16-40+21=-3$
For $x=-3$: $y=(-3)^2 +10(-3)+21=9-30+21=0$
Right points: $(-4,-3), (-3,0)$

Answer:

Five points to plot:

1. Vertex: $(-5, -4)$
2. Left of vertex: $(-7, 0)$, $(-6, -3)$
3. Right of vertex: $(-4, -3)$, $(-3, 0)$

Connect these points to graph the parabola.