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

vertex is (6 , -9)

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

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 =(-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 =(-b)/(2a)=(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.