Which quadratic function is best represented by this graph? f(x)=x2+6x+8

f(x)=x2−6x−8

f(x)=x2+8

f(x)=x2−6x+8

Given:  

f

(

x

)

=

x

2

−

6

x

+

8

This function is a quadratic - a graph of a parabola.

Factor and let  

f

(

x

)

=

0

to find the x-intercepts :

x

2

−

6

x

+

8

=

(

x

−

2

)

(

x

−

4

)

=

0

#x - 2 = 0 " "=> x = 2; " "x - 4 = 0 " "=> x = 4

x

-intercepts: " "(2, 0), (4, 0)#

Find the y-intercept let  

x

=

0

:

f

(

0

)

=

0

2

−

6

⋅

0

+

8

=

0

y

-intercept: " "(0, 8)#

Find the vertex . When the equation is in  

A

x

2

+

B

x

+

C

=

0

,

the vertex is  

(

−

B

2

A

,

f

(

−

B

2

A

)

)

−

B

2

A

=

6

2

=

3

f

(

3

)

=

3

2

−

6

⋅

3

+

8

=

−

1

vertex:  

(

3

,

−

1

)

Plot a couple of other points using point-plotting. Since  

x

is the independent variable, you can select any  

x

and calculate the corresponding  

y

:

x

∣

y

−−−−−−−−−−−−−  

1

∣

3

5

∣

3

6

∣

8

graph{x^2 -6x + 8 [-5, 10, -2, 10]}

Step-by-step explanation:

1. 34

2. 268

3. x=14.4

step-by-step explanation:

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: