The graph of the quadratic function $y = ax^2 + bx + c$ $(a \neq 0)$ intersects the $x$-axis a

Question

The graph of the quadratic function $y = ax^2 + bx + c$ $(a \neq 0)$ intersects the $x$-axis at $A$ and $B$ ; intersects the $y$-axis at $C$. It is given that $AC = \sqrt{10}$ and $OB = OC = 3OA$. Find the values of $a$, $b$ and $c$. Find the coordinates of a point $P$ on the part of the graph of $y = ax^2 + bx + c$ that is in the $2^{\text{nd}}$ quadrant, such that the area of quadrilateral $PBAC$ is a maximum. Hence find this maximum of area in the exact form.

Accepted Answer

(a) $a=-1$, $b=-2$, $c=3$ (b) $P\left( -\frac{3}{2},\frac{15}{4} \right)$, $9\frac{3}{8}$ units$^{2}$

Coordinate Geometry

Coordinate Geometry