Question

graph the function $f(x) = -3x^2 + 12x - 9$. 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 $f(x)=ax^2+bx+c$, $x=-\frac{b}{2a}$
$x=-\frac{12}{2(-3)} = 2$

Step2: Find vertex y-coordinate

Substitute $x=2$ into $f(x)$
$f(2)=-3(2)^2+12(2)-9 = -12+24-9=3$

Step3: Find another point

Choose $x=0$, substitute into $f(x)$
$f(0)=-3(0)^2+12(0)-9=-9$

Answer:

1. Vertex: $(2, 3)$
2. Additional point: $(0, -9)$

(Plot these two points and draw a downward-opening parabola through them; the parabola also passes through $(4, -9)$, symmetric to $(0, -9)$ about the vertex)