Help I am trying to study for a test....
given the following function f(x)=2x^2-4x-5\
1) determine the vertex
2) list the axis of symmetry
3) calculate the y-intercept
4) use the axis of symmetry and the y-intercept to find an additional point on the graph

- anonymous

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- Mertsj

Do you know that it's a parabola?

- anonymous

No that is all the study paper give us was this ? exactly like it is

- Mertsj

What have you been studying in your class?

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- anonymous

This is the start of the class and we are having to take a pretest

- anonymous

it is college algebra or precalculus

- Mertsj

well then your teacher is trying to find out what you know so just do the best you can.

- anonymous

well out textbook does not really give a good explanation of anything

- Mertsj

So do you want to work through this problem?

- anonymous

i would appreciate any help i can get

- Mertsj

This is the equation of a parabola. The x coordinate of the vertex can be found using the formula x = -b/2a

- Mertsj

which in this case is 4/4 or 1

- Mertsj

Now you can find the y coordinate of the vertex by replacing x with 1 and finding f(x)

- Mertsj

f(1)=-7 So the vertex is (1,-7)

- anonymous

so how do u come up with the 7

- Mertsj

The axis of symmetry is the vertical line through the vertex so it is x = 1

- Mertsj

Did you replace x with 1 in your equation?

- anonymous

o no

- Mertsj

\[f(x)=2(1)^2-4(1)-5=2-4-5=2-9=-7\]

- Mertsj

Are you reading what I write?

- Mertsj

Now you can find the y coordinate of the vertex by replacing x with 1 and finding f(x)

- anonymous

yes I am

- Mertsj

So now we are ready for 3 which is calculate the y intercept. We can find the y intercept by letting x = 0. So replace x with 0

- Mertsj

Did you get -5? So the y intercept is (0,-5)

- anonymous

just a sec

- Mertsj

one second granted

- anonymous

ok 0 cancels so i end up with -5

- Mertsj

Yep

- Mertsj

Now we're ready for the last part. And for that we need to put the info we have on a graph.

- Mertsj

|dw:1328758359627:dw|

- Mertsj

The axis of symmetry helps us find another point because for every point to the left of the axis, there is a corresponding point to the right.

- Mertsj

So if we start at the y intercept and go 1 unit to the right, we come to the aos. If we go one more unit to the right, there will be another point.

- Mertsj

|dw:1328758665785:dw|

- Mertsj

So another point on the graph is (2,-5)

- anonymous

so unless it is stated you either move to the left or right 1 point

- Mertsj

You move however many units it takes to get to the axis of symmetry.

- anonymous

o ok...thank u for ur help

- Mertsj

yw

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