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

Refer the attached figure.

Step-by-step explanation:

Given : The quadratic equation -  

To find : The graphic representation of the quadratic function ?

Solution :

We plot the graph of quadratic equation,

The standard form of equation is

Comparing with given equation,

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

Axis of symmetry is  

The axis of symmetry of given equation is

The vertex form of quadratic equation is

Where, (h,k) are the vertex.

Convert the quadratic equation into vertex form,

By completing the square,

On comparison,

(h,k)=(4,8)

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

Refer the attached figure below.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c