## CSMC 2022 Part B - Question 1, CEMC UWaterloo

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#### Difficulty: 5

#### This problem is tagged with csmc, csmc22, highschool.

**(Canadian Senior Mathematics Contest 2022, Part B, Question 1, CEMC - UWaterloo)**

The parabola with equation $y = −x^2 + 16$ intersects the x-axis at points $A$ and $B$
and the horizontal line with equation $y = 7$ at points $M$ and $N$, as shown.

a) Determine the coordinates of $A$ and $B$.

b) Determine the area of the trapezoid $MNBA$.

c) Suppose that $O$ is the origin and $V$ is the vertex of the parabola. The line $y = −33$ intersects the parabola at points $P$ and $Q$. Determine the area of quadrilateral $VPOQ$, which is shaded in the diagram below.

*Answer Submission Note(s)*

Your answer for the first part should be point $A$ followed by point $B$, in the form "(x1,y1),(x2,y2)". The answer for the other two parts should be integers. The final answer should have all three answers space-separated and in order.

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