Question

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

Answer 1

Do you know that it's a parabola?

Answer 2

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

Answer 3

What have you been studying in your class?

Answer 4

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

Answer 5

it is college algebra or precalculus

Answer 6

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

Answer 7

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

Answer 8

So do you want to work through this problem?

Answer 9

i would appreciate any help i can get

Answer 10

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

Answer 11

which in this case is 4/4 or 1

Answer 12

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

Answer 13

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

Answer 14

so how do u come up with the 7

Answer 15

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

Answer 16

Did you replace x with 1 in your equation?

Answer 17

o no

Answer 18

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

Answer 19

Are you reading what I write?

Answer 20

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

Answer 21

yes I am

Answer 22

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

Answer 23

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

Answer 24

just a sec

Answer 25

one second granted

Answer 26

ok 0 cancels so i end up with -5

Answer 27

Yep

Answer 28

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