Question

A diver dives from the 3 m board at a swimming pool. Her height, y, in metres, above the water in terms of her horizontal distance, x, in metres, from the end of the board is given by y= -x^2 + 2x + 3. What is the diver's maximum height?

Answer 1

The maximum height of the diver would be the y value of the vertex of the graph. The vertex of the graph is (1,4). The maximum height of the diver is 4 meters.

Answer 2

Maximum height of the diver is 4 meter

What is parabola?

a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped

What is Vertex of a parabola?

The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry

Vertex of the parabola =$a(x-h^{2})+k$

standard form of the parabola $y=ax^{2} +bx+3$

Given that $y=-x^{2} +2x+3$

Group and factor the equations

$y=(-x^{2} +2x)+3\\y=-(x^{2} -2x)+3$

Then, add and subtract 1 in the bracket

$y=-(x^{2} -2x+1-1)+3\\y=-(x^{2} -2x+1)+1+3\\y=-(x^{2} -2x+1)+4$

Simplify the equation

$y=-(x-1)^{2}+4$

Therefore

Height of the diver is 4meter, because vertex of the parabola is (1,4)

Hence, the height of the diver is 4 meter

Learn more about Parabola and Vertex of the parabola here

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