Parabola through the axis intercepts of a line and the area enclosed between them
Parabola through the axis intercepts of a line and the area enclosed between them
7 marks
The line \(y=12-6x\) meets the \(y\)-axis at \(M(0,12)\) and the \(x\)-axis at \(N(2,0)\). The curve \(y=ax^2+c\), where \(a\) and \(c\) are integers, also passes through \(M\) and \(N\), as shown in the diagram.
- Write down \(c\).
- Find \(a\).[3]
The region bounded by the line and the curve is shaded in the diagram below.
- Find the exact area of the region shaded in the second diagram.[4]
Solution:
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Answer:(a)(i) \(c=12\) (a)(ii) \(a=-3\) (b) \(4\text{ units}^2\)
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