Maths question

f(x)=(x-1)(x+2) So its a parabola which crosses the x axis at 1 and -2 obviously.

for part one you shift it 2 to the left so now the x intercepts become -4 and -1.

If you don't see how to draw f(x) expand it it may help.

I LOVE YOU.
i understand, thank you so much
I knew you had to do something with the equation they gave

I thought I was supposed to shift this 2 spaces to the left?
Question 2Bi

for 2a did you draw something that looked a little like this;

no problem, just get used to reading these types of questions. You knew how to do it, i could tell. If you need any help with AS maths you can PM me. I finished A level maths and got 98% at AS.

Yes thats correct, you just make x-1=0 and x+2=0
you get 1 & -2

the y intercept is -1x2 (-2)
and then plot

ah someones already helped you, I was just going to say how from this graph is easy to see how shifting everything to the left bt two will give you the graph shown in the answer book

I will. I know how to do fx notation with exam solutions but this answer in the textbook doesn't even make sense

did you get an A/A* in maths a level?
i'm doing 6 units this year!! tips?

I took C1-4 FP1-2 if you need any help just pm

Posted from TSR Mobile

thanks anyway
for 2bii) f(x) + 2
I shift 2 unit up right?

and do I start originally from the f(x) = (x-1) (x+2) sketch?

yea thats exactly what you do

and you do start with (x-1)(x+2) yea

basically when you were doing f(x+2) what you are actually doing when you "shift the graph two units to the left" is replacing all the "x"s you see in the function with "x + 2"s.

Think of it like this, if f(x) = (x-1)(x+2)
then you could also say, f(q) = (q-1)(q+2)
or if you really wanted, f() = (-1)(+2) where just like x and q, the just represents a number

so if you have f(x+2) you get ((x+2)-1)((x+2)+2) = (x+1)(x+4). This is what you drew in part 2b)i).

Then with f(x) + a, you just write down your function, in this case f(x) is (x-1)(x+2) and stick + a on the end

So, f(x) + a = (x-1)(x+2) + a

And in your case f(x) + 2 = (x-1)(x+2) + 2, which results in the shift upwards of 2 units when you draw the graph

I understand now.
but is this the answer?
shouldn't i be back at 0 not going thru it?

$\displaystyle f(x) = (x-1)(x+2)$
$\displaystyle f(x) + 2 = (x-1)(x+2) + 2$
$\displaystyle f(x) + 2 = x^2 + x - 2 + 2$
$\displaystyle f(x) + 2 = x^2 + x = x(x+1)$

therefore f(x) + 2 crosses the x axis at x=0 and x=-1 as the answer scheme shows

Ah i feel so dumb, I get the first two but when you expand the bracket how comes you dont do it properly?

dont do it properly. how do you mean? did you learn to expand brackets with FOIL?

i got this by foil
x2 + 2x - x -2 +2

x2 + x -2 +2 ?

oh sorry, maybe I should have done it like this;

$\displaystyle f(x) + 2 = (x-1)(x+2) + 2$
$\displaystyle f(x) + 2 = (x^2 + 2x - x - 2) + 2$

Now I just simplify the x terms ie simplfy $\displaystyle 2x - x$

$\displaystyle f(x) + 2 = (x^2 + x - 2) + 2$

Is that easier to see now?

Now from here you have $\displaystyle f(x) + 2 = (x^2 + x - 2) + 2$

do you see how the -2 and + 2 "cancel out" leaving you with;

$\displaystyle f(x) + 2 = x^2 + x$

now factoring out an x gives us $\displaystyle f(x) + 2 = x(x + 1)$

thanks so much
I got f(x) +2 = x2 + x
and then i factorise to get x(x+1)
make x = 0
I'm left with x=-1 and x=0?
thanks for the time

oh sorry, maybe I should have done it like this;

$\displaystyle f(x) + 2 = (x-1)(x+2) + 2$
$\displaystyle f(x) + 2 = (x^2 + 2x - x - 2) + 2$

Now I just simplify the x terms ie simplfy $\displaystyle 2x - x$, and im left with;

$\displaystyle f(x) + 2 = (x^2 + x - 2) + 2$

Is that easier to see now?

Now from here you have $\displaystyle f(x) + 2 = (x^2 + x - 2) + 2$

do you see how the -2 and + 2 "cancel out" leaving you with;

$\displaystyle f(x) + 2 = x^2 + x$

now factoring out an x gives us $\displaystyle f(x) + 2 = x(x + 1)$