3. The picture shows a water fountain in a park. The water follows a path in the shape of a parabola. The equation of the water path is
y=-x^2+4x+2, where y is the height of the water above the pond level
and x is the horizontal distance of the water from the fountain outlet
a
Estimate the maximum height of the water. Show how you
determined your answer.
b. Approximately how far from the outlet will the water's path be when
the water reaches pond level? Use the quadratic formula to find your
answer. Show your work,

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solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.