Question

graph the function f(x) = 6x² + 12x + 7.
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.
graph with x-axis from -10 to 10 and f(x)-axis from -10 to 10, grid lines, and axes labeled
submit

Explanation:

Step1: Find vertex x-coordinate

For $ax^2+bx+c$, $x=-\frac{b}{2a}$
$x=-\frac{12}{2(6)}=-1$

Step2: Find vertex y-coordinate

Substitute $x=-1$ into $f(x)$
$f(-1)=6(-1)^2+12(-1)+7=6-12+7=1$

Step3: Find a second point

Choose $x=0$, substitute into $f(x)$
$f(0)=6(0)^2+12(0)+7=7$

Answer:

1. Vertex point: $(-1, 1)$
2. Second point: $(0, 7)$

To graph: Plot $(-1, 1)$ as the vertex, then plot $(0, 7)$. Reflect $(0, 7)$ across the axis of symmetry $x=-1$ to get a third point $(-2, 7)$, then draw a smooth upward-opening parabola through these points.