<p>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&nbsp;\(AC = \sqrt{10}\) and \(OB = OC = 3OA\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the values of \(a\), \(b\) and \(c\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">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.</span></div></li></ol>
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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.

Coordinate Geometry

Question a7e19a6a