Question

graph the function $f(x) = 2x^2 + 8x + 14$. 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.

Explanation:

Step1: Find vertex x-coordinate

For $f(x)=ax^2+bx+c$, $x=-\frac{b}{2a}$. Here $a=2$, $b=8$:
$x=-\frac{8}{2\times2}=-2$

Step2: Find vertex y-coordinate

Substitute $x=-2$ into $f(x)$:
$f(-2)=2(-2)^2+8(-2)+14=2(4)-16+14=8-16+14=6$
Vertex is $(-2,6)$.

Step3: Find another point

Choose $x=0$, substitute into $f(x)$:
$f(0)=2(0)^2+8(0)+14=14$
Point is $(0,14)$.

Answer:

Vertex: $(-2, 6)$; Additional point: $(0, 14)$
(To graph, plot $(-2,6)$ as the vertex, then plot $(0,14)$, and draw a symmetric upward-opening parabola through these points.)