SOLUTION: Sketch the graph of f(x) = x^2-6x +8. Label all x-intercept, y-intercepts and the vertex.

Question 128198: Sketch the graph of f(x) = x^2-6x +8. Label all x-intercept, y-intercepts
and the vertex.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given function

To find the x-intercept, let

Plug in

Factor the right side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So the x-intercepts are (2,0) and (4,0)

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To find the y-intercept, plug in

Start with the given function

Plug in

Raise 0 to the 2nd power to get 0

Multiply 1 and 0 to get 0

Multiply 6 and 0 to get 0

Subtract 0 from 0 to get 0

Add 0 and 8 to get 8

So when , we have

So this means that the y-intercept is (0,8)

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To find the vertex, we first need to find the axis of symmetry (ie the x-coordinate of the vertex)
To find the axis of symmetry, use this formula:

From the equation we can see that a=1 and b=-6

Plug in b=-6 and a=1

Negate -6 to get 6

Multiply 2 and 1 to get 2

Reduce

So the axis of symmetry is

So the x-coordinate of the vertex is . Lets plug this into the equation to find the y-coordinate of the vertex.

Lets evaluate

Start with the given polynomial

Plug in

Raise 3 to the second power to get 9

Multiply 6 by 3 to get 18

Now combine like terms

So the vertex is (3,-1)

So putting all of this together, we get

Graph of

and we can see that the x-intercepts are (2,0) and (4,0), the graph has the y-intercept (0,8), and the vertex is (3,-1). So this visually verifies our answer.
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