Question

given the quadratic function f(x) = x^2- x-6.determine the x-intercepts for y= f(2x)

Answer 1

firstly find the x-intercepts of f(x) - do you know how?

Answer 2

yeah by factoring rite?

Answer 3

correct - so what do you get for this?

Answer 4

(x-3) (x+2)

Answer 5

that is the correct factorisation - now do you know how to find the x-intercepts from this?

Answer 6

umm..no

Answer 7

oh wait, u mean 3 and -2?

Answer 8

think about what happens to the curve at the x-intercepts. what do you think will be the value of y when the curve touches the x-axis?

Answer 9

yes = you have the right values there :)
now - do you know what to do next?

Answer 10

nope :(

Answer 11

think about the graph of y=f(x) and that of y=f(2x)

Answer 12

okay

Answer 13

for y=f(2x), the value of x would need to be halved in order to get the equivalent point on y=f(x)

Answer 14

rite

Answer 15

therefore the x-intercepts for y=f(2x) will be half of the x-intercepts for y=f(x)

Answer 16

given that - what do you think will be the x-intercepts for y=f(2x)?

Answer 17

isnt it zero? not sure

Answer 18

what values did you get for the x-intercepts for y=f(x) - look above

Answer 19

oh 3 and -2

Answer 20

so is it 1.5 and -1?

Answer 21

good - so what should the x-intercepts of y=f(2x) be?

Answer 22

thats it - well done! :)

Answer 23

oh i get it know, so if it was say y=f(4x) rite what would have been the x interepts

Answer 24

what do you think?

Answer 25

now*

Answer 26

x intercepts would be 3/4 and -2/4

Answer 27

yes :)

Answer 28

oh okay thanks soo much :)

Answer 29

yw :)