Answer:
Refer the attached figure.
Step-by-step explanation:
Given : The quadratic equation - [tex]f(x)=x^2-8x+24[/tex]
To find : The graphic representation of the quadratic function ?
Solution :
We plot the graph of quadratic equation,
The standard form of equation is [tex]y=ax^2+bx+c[/tex]
Comparing with given equation, [tex]f(x)=x^2-8x+24[/tex]
a=1 , b=-8 , c=24
Axis of symmetry is [tex]x=-\frac{b}{2a}[/tex]
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^2-8x+24[/tex]
[tex]f(x)=(x^2-2(4)x+(4)^2)-(4)^2+24[/tex]
[tex]f(x)=(x-4)^2+8[/tex]
On comparison,
(h,k)=(4,8)
Now, we plot the equation with vertex (4,8).
Refer the attached figure below.
