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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
Reply 1
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.
Reply 2
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.
Reply 3
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)

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