Question: An expression is shown below: f(x) = x^2 – 6x + 5 Part A: What are the x-intercepts of the graph of f(x)? Show your work.

Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work.

Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.

given a parabola in standard form

y

=

a

x

2

+

b

x

+

c

then the x-coordinate of the vertex can be found using

∙

x

x

vertex

=

−

b

2

a

y

=

x

2

−

6

x

+

5

is in standard form

with

a

=

1

,

b

=

−

6

,

c

=

5

⇒

x

vertex

=

−

−

6

2

=

3

substitute this value into equation for y-coordinate

y

vertex

=

3

2

−

6

(

3

)

+

5

=

−

4

⇒

vertex

=

(

3

,

−

4

)

the axis of symmetry is vertical and passes through the

vertex with equation

x

=

3

to find x-intercepts let y = 0

⇒

x

2

−

6

x

+

5

=

0

the factors of + 5 which sum to - 6 are - 1 and - 5

⇒

(

x

−

1

)

(

x

−

5

)

=

0

equate each factor to zero and solve for x

x

−

1

=

0

⇒

x

=

1

x

−

5

=

0

⇒

x

=

5

⇒

x

=

1

and

x

=

5

←

x-intercepts

graph{(y-x^2+6x-5)(y-1000x+3000)=0 [-10, 10, -5, 5]}

answer

see attachment

explanation

the given function is

this function has y-intercept at

-4 and a slope of 2.

note that, the graph has a positive slope.

the graph that represents this function is the straight line that moves upward from left to right.

the graph touches the y-axis at -4.

the correct choice is the graph shown in the attachment.