Question

Use the parabola tool to graph the quadratic function f(x)=x2−12x+27.

Answer 1

Remember that for a quadratic function of the form $a x^{2} +bx+c$ we can find its vertex with formula: $h= \frac{-b}{2a}$ where $h$ is the x-coordinate of the vertex; then we will find the y-coordinate by replacing $h$ in our original function.

From the question know that $a=1$ and $b=-12$, so lets replace those values in our vertex formula to find the x-coordinate of our vertex:
$h= \frac{-(-12)}{2(1)}$
$h= \frac{12}{2}$
$h=6$
Now lets replace that value into our original function to find the y-coordinate of our vertex:
$f(6)=6^{2} -12(6)+27$
$f(6)=36-72+27$
$f(6)=-9$
Finally, we have our vertex (6,-9)

Now to graph our function we are going to take advantage of its line of symmetry; if the vertex is (6,-9) the line of symmetry of the parabola is x=6, so if we chose the point (6,0), our second point will have coordinates (3,0) as you can see in the picture.