Originally Posted by
Moo Hello,
If one point is on the x-axis, then y=0. So the point (3,0) is a point on the curve.
If it "touches" the x axis at x=9/4, it means that the x axis is tangent to the curve at this point.
This means two things :
- the derivative at this point is 0. Mr F adds: If you haven't done calculus, this means that there's a turning point at this point.
- the point (9/4,0) is a point on a curve.
Mr F adds: In case you haven't done calculus ..... when a cubic function has a turning point at the x-intercept ( $\displaystyle {\color{red}\alpha}$, 0) this means that $\displaystyle {\color{red}(x - \alpha)^2}$ is a factor of the cubic.
Now, substitute all this information in the equation. It should give you 3 equations with 3 unknowns.