Question

Choose the graphic representation of the quadratic function f(x)=x^2-8x+24

Answer 1

The Answer is ----D----

Answer 2

Answer:

Refer the attached figure.

Step-by-step explanation:

Given : The quadratic equation -  $f(x)=x^2-8x+24$

To find : The graphic representation of the quadratic function ?

Solution :

We plot the graph of quadratic equation,

The standard form of equation is $y=ax^2+bx+c$

Comparing with given equation, $f(x)=x^2-8x+24$

a=1 , b=-8 , c=24

Axis of symmetry is  $x=-\frac{b}{2a}$

The axis of symmetry of given equation is $x=-\frac{-8}{2(1)}=4$

The vertex form of quadratic equation is $f (x) = a(x - h)^2 + k$

Where, (h,k) are the vertex.

Convert the quadratic equation into vertex form,

By completing the square,

$f(x)=x^2-8x+24$

$f(x)=(x^2-2(4)x+(4)^2)-(4)^2+24$

$f(x)=(x-4)^2+8$

On comparison,

(h,k)=(4,8)

Now, we plot the equation with vertex (4,8).

Refer the attached figure below.