graph the parabola.\n$y = x^2 + 10x + 21$\nplot five points on the parabola: the vertex, two points to the…

graph the parabola.\n$y = x^2 + 10x + 21$\nplot 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.

graph the parabola.\n$y = x^2 + 10x + 21$\nplot 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.

Answer

Explanation:

Step1: Find vertex x-coordinate

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

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: Find left points (x=-7, -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: Find right points (x=-4, -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:

Plot the following 5 points:

  1. Vertex: $(-5, -4)$
  2. Left points: $(-7, 0)$, $(-6, -3)$
  3. Right points: $(-4, -3)$, $(-3, 0)$ Then connect the points to graph the parabola.