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Can someone help me with this question? (further maths)

The curve with equation y=ax^2+bx+c passes through the points P(2,6) and Q(3,16), and has a gradient of 7 at the point P. Find the values of the constants a, b, and c.

Help would be much appreciated :smile:

Reply 1

DFranklin

When x = 2, what does y equal? So what must a2^2 + 2b + c equal?
Similarly for x =3.
Also, at x=2, what does dy/dx equal. So ...

Reply 2

looloo59

Original post by DFranklin

When x = 2, what does y equal? So what must a2^2 + 2b + c equal?
Similarly for x =3.
Also, at x=2, what does dy/dx equal. So ...

I'm still quite confused :confused:

I've worked out that 4a+2b+c=6 and 9a+3b+c=16 but now what? dy/dx when x=2 is 7 but I dont know what to do with that information :frown:

Reply 3

DFranklin

Well, if y = ax^2+bx+c, then what is dy/dx?

Reply 4

jit987

Differentiate the equation with the unknowns and sub in the appropriate 'x' value, what should that equal to?

Reply 5

looloo59

Original post by DFranklin

Well, if y = ax^2+bx+c, then what is dy/dx?

so dy/dx=2ax+b, when x=2 dy/dx=4a+b so 4a+b=7 ???

Reply 6

DFranklin

Yes. So you now have 3 equations in 3 unknowns, which is enough to solve for a, b and c. (Start by noting that b = 7-4a, so you can replace b by (7-4a) in the two other equations).

Reply 7

looloo59

Original post by DFranklin

Yes. So you now have 3 equations in 3 unknowns, which is enough to solve for a, b and c. (Start by noting that b = 7-4a, so you can replace b by (7-4a) in the two other equations).

Thankyou

that makes a lot more sense now... I'm very new to a-level maths :P

Reply 8

looloo59

Original post by looloo59

Original post by DFranklin

Yes. So you now have 3 equations in 3 unknowns, which is enough to solve for a, b and c. (Start by noting that b = 7-4a, so you can replace b by (7-4a) in the two other equations).