The diagram shows two quadratic curves, $y = -\frac{1}{2}x^2 + 2x$ and \(y = -\frac{1}{2}x^2 - x +

Question

The diagram shows two quadratic curves, $y = -\frac{1}{2}x^2 + 2x$ and $y = -\frac{1}{2}x^2 - x + 3$, which intersect each other at $C$. A straight line touches both quadratic curves at only one point, $A$ and $B$, respectively.
Find

the equation of the straight line in the form of $y = mx + c$.[6]
the coordinates of $A$, $B$ and $C$.[3]
the exact area of triangle $ABC$.[2]

Accepted Answer

(a) $y=-\frac12x+\frac{25}{8}$ (b) $A=\left(-\frac12,\frac{27}{8}\right)$, $B=\left(\frac52,\frac{15}{8}\right)$, $C=\left(1,\frac32\right)$ (c) $\frac{27}{16}\text{ units}^2$

IP3 Class Test (May 2025) Bonus Question

IP3 Class Test (May 2025) Bonus Question

Video Solution:

Solution:

Solution locked