The curve C has equation: y = x2 + ax + b

Given that the minimum point of C has coordinates (−2, 5), find the values of a and b.

How would you tackle a question like this?

Reply 1

lewisfish

diff the equation then set dy/dx to 0 as stat. point then sub in x to find a. then sub in x,y and a values into original equation to find b

Reply 2

Sasukekun

If it's a minimum point then the gradient is zero. If you're at the stage in maths where you differentiate, differentiate the equation. This'll give you the gradient in terms of x and a, and since you know that the gradient is zero you can find a, and then b after that.

I won't go in to detail, but I got A as 4, and B as 9. Maybe I'm wrong.

Reply 3

roar558

dy/dx=k(x+2)
integrate this, substitute to find the equation of the curve
tip
If the curve's equation is y=x^2... how do you find k?

Reply 4

Connor132

You need to set the equation out as y=(x+p)^2 +q

so (x+1/2a)^2 +b - 1/2a^2

(x+2)^2 +5 then multiply it out to get x^2 + 4x + 9

Sorry about the poor explaination, but it's hard on a keyboards.

Just remember the minium point is (-a, b) when the equation is in the form (x+a)^2+b = 0