Question

Which function has a vertex on the y-axis?
a) f(x) = (x – 2)2
b)f(x) = x(x + 2)
c)f(x) = (x – 2)(x + 2)
d)f(x) = (x + 1)(x – 2)

Answer 1

That means which ever one's x coordinate for the vertex is 0, will have it's vertex on the y axis.

Answer 2

Try calculating the last 2 using
(p+q)/2 for the x coordinate
p,q=x intercepts

Answer 3

ok one moment @dtan5457

Answer 4

ok i got lost im not sure how to do it @dtan5457

Answer 5

p,q=x axis intercepts

f(x) = (x – 2)(x + 2)
p=2
q=-2

f(x) = (x + 1)(x – 2)
p=-1
q=2

Answer 6

use (p+q)/2 and which ever one turns out to be 0 is your answer

Answer 7

im not sure how to use the (p+q)/2 form @dtan5457

Answer 8

I just gave you the p and q values. just plug them in

Answer 9

wait so it would be(2-2) (-2+2) @dtan5457

Answer 10

@butterflydreamer

Answer 11

@pitamar

Answer 12

Remember the last problem? you have to find the vertex position of each one of those functions.
Remember that if the function has 2 roots, then the vertex will be in their middle. if it has one root then this is the vertex. (you don't have here cases without roots).
The root is basically a point where the function gives a value of 0 ( f(x) = 0 ).
Can you tell for what 'x' values the first function gives a value of 0?

Answer 13

so instead im adding 0 like this f(o)=(0-2)(0+2) @pitamar

Answer 14

Not exactly. you basically wanna do something of the kind
$$f(x)=0\implies (x-2)2 = 0
$$ and find what value x will make it true.
Those values of 'x' that function value is 0 for are the 'roots' of the functions.

Answer 15

so it would be 2? @pitamar

Answer 16

Exactly. that is the single root of this function =)
Not other value of 'x' will make this equation true.
That means that the vertex is at x=2. You can find the y value for that vertex if you want, but the question is:
`What function has a vertex on the y-axis?`
The y-axis is basically at x=0. This vertex is not in x=0, so this function cannot be the answer

Answer 17

so the answer is not c? @pitamar

Answer 18

The answer is C =)
The roots are 2 and -2 and the middle of those values is indeed 0.

Answer 19

okay gotcha thanks :) @pitamar

Answer 20

Np =)