a) Differentiate y=x^2+bx+c, and hence find b and c, given that the parabola is tangent to the x-axis at the point (5,0)
b) Differentiate y=x^2+bx+c, and hence find b and c, when x =3 the gradient is 5, and x=2 is a zero.
Because the parabola is a tangent at that point. A parabola can only ever be a tangent to the x axis if it has it's vertex at a point on the x axis. It can never touch it twice in that case because it's an increasing function only.How can you be sure that the gradient at the x-axis is always 0? Like if it cuts the x axis twice, then wouldn't it have a non-zero gradient?
Ah mb, didn't read that the parabola was a tangent to the x-axisBecause the parabola is a tangent at that point. A parabola can only ever be a tangent to the x axis if it has it's vertex at a point on the x axis. It can never touch it twice in that case because it's an increasing function only.
so for part b)
ThanksIm pretty sure when it says that x=2 is a zero, it means that its an intercept, such that when x=2, y=0.