# Higher Maths Curve question

The diagram shows the curve with equation y f = (x), where
f (x)= kx(x+a)(x+b)
The curve passes through (-1,0), (0,0), (1,2) and (2,0)

theres a graph but i cant paste it here.

Find the values of a, b and k.

This is a paper 1 Exemplar paper 2015
Original post by sirennity
The diagram shows the curve with equation y f = (x), where
f (x)= kx(x+a)(x+b)
The curve passes through (-1,0), (0,0), (1,2) and (2,0)

theres a graph but i cant paste it here.

Find the values of a, b and k.

This is a paper 1 Exemplar paper 2015

You have 3 unknowns and 4 points, so sub them in and see if you can solve for their values.
In particular, think about which points corrrespond to roots of the function.
thing is im not sure what exactly are roots. i think its the points that lie on the X axis right? if so then it will be -1 and 2. In my notes booklet I have an example like that but theres 3 brackets and in the formula that the queation gave me theres only 2, so do i just add a 3rd one in for point (1,2)? im confused

Original post by mqb2766
You have 3 unknowns and 4 points, so sub them in and see if you can solve for their values.
In particular, think about which points corrrespond to roots of the function.
Original post by sirennity
thing is im not sure what exactly are roots. i think its the points that lie on the X axis right? if so then it will be -1 and 2. In my notes booklet I have an example like that but theres 3 brackets and in the formula that the queation gave me theres only 2, so do i just add a 3rd one in for point (1,2)? im confused

The roots are when the curve crosses the x-axis, so when the y-value of the function is zero, so they correspond to -1 and 2 as you say. That means two of the given points allow you to "write down" the values of a and b.

For k, sub the third (x,y) value into the function and solve for k.
(edited 2 years ago)