Question

Use the parabola tool to graph the quadratic function f(x)=x2−12x+27. Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Answer 1

Answer:

vertex is (6 , -9)

points are (9,0) and (3,0)

Step-by-step explanation:

Given quadratic function $f(x)=x^2-12x+27$

We have to plot the given quadratic function.

Consider the Given quadratic function $f(x)=x^2-12x+27$

The general form of quadratic function  is given $f(x)=a(x-h)^2+k$

Where, (h, k)  is vertex , given  $h =\frac{-b}{2a}$ and $k = f(h)$  

Thus, for given quadratic function $f(x)=x^2-12x+27$

a = 1 , b= -12 , c = 27

Thus,

$h =\frac{-b}{2a}=\frac{12}{2}=6$

$k = f(h)$ that is f(12) = (6)^2 - 12× 6 +27 = 36 - 72 + 27 = - 9

Thus, given  quadratic function $f(x)=x^2-12x+27$ in standard form is $f(x)=(x-6)^2-9$  

Thus, vertex is (6 , -9)

For second point put $f(x)=0$  , we get,

$f(x)=(x-6)^2-9=0$  

$\Rightarrow (x-6)^2-9=0$  

$\Rightarrow (x-6)^2=9$  

$\Rightarrow (x-6)=\pm 3$  

$\Rightarrow x= 6\pm 3$  

Thus, $\Rightarrow x=6+3=9$ and $\Rightarrow x=6-3=3$  

thus, points are (9,0) and (3,0)

Graph is attached below.