Answer :
Refer the attached figure for the graphic representation of the given quadratic equation.
Step-by-step explanation:
Given expression:
[tex]f(x)=x^{2}-8 x+24[/tex]
To find:
The graphic representation of the given quadratic function
For solution, plot the graph to the given quadratic equation.
The standard form of the equation is
[tex]y=a x^{2}+b x+c[/tex]
When comparing with given quadratic equation,
a = 1, b = - 8, c = 24
Axis of symmetry is [tex]x=\frac{-b}{2 a}[/tex]
By applying the values, the axis of symmetry of given equation is
[tex]x=\frac{-(-8)}{2(1)}=4[/tex]
The vertex form of quadratic equation is [tex]f(x)=a(x-h)^{2}+k[/tex]
Where, (h,k) are the vertex.
Convert the quadratic equation into vertex form.
By completing the square,
[tex]f(x)=x^{2}-8 x+24[/tex]
[tex]f(x)=\left(x^{2}-2(4) x+4^{2}\right)-4^{2}+24[/tex]
[tex]f(x)=(x-4)^{2}+8[/tex]
On comparison,
(h , k) = (4 , 8)
Now, plot the equation with vertex (4,8) [refer attached figure].
