Question

graph the parabola.
$y=3x^{2}+18x+23$
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 $y=ax^2+bx+c$, $x=-\frac{b}{2a}$
$x=-\frac{18}{2(3)}=-3$

Step2: Find vertex y-coordinate

Substitute $x=-3$ into equation:
$y=3(-3)^2+18(-3)+23=3(9)-54+23=27-54+23=-4$
Vertex: $(-3, -4)$

Step3: Left point 1 (x=-4)

$y=3(-4)^2+18(-4)+23=3(16)-72+23=48-72+23=-1$
Point: $(-4, -1)$

Step4: Left point 2 (x=-5)

$y=3(-5)^2+18(-5)+23=3(25)-90+23=75-90+23=8$
Point: $(-5, 8)$

Step5: Right point 1 (x=-2)

$y=3(-2)^2+18(-2)+23=3(4)-36+23=12-36+23=-1$
Point: $(-2, -1)$

Step6: Right point 2 (x=-1)

$y=3(-1)^2+18(-1)+23=3(1)-18+23=3-18+23=8$
Point: $(-1, 8)$

Answer:

Five points to plot:

1. Vertex: $(-3, -4)$
2. Left of vertex: $(-4, -1)$, $(-5, 8)$
3. Right of vertex: $(-2, -1)$, $(-1, 8)$

Connect these points to graph the parabola.