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The function y=-0.2x^2+1.9x models the path of a kicked soccer ball.The height is y,the distance is x, and the units are meters.How high does the soccer ball go?

User Yuda
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1 Answer

2 votes

Answer:

The highest height the ball achieves is 4.5125 meters.

Explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:


f(x) = ax^(2) + bx + c

It's vertex is the point
(x_(v), y_(v))

In which


x_(v) = -(b)/(2a)


y_(v) = -(\Delta)/(4a)

Where


\Delta = b^2-4ac

If a<0, the vertex is a maximum point, that is, the maximum value happens at
x_(v), and it's value is
y_(v).

In this question:

Quadratic function
y = -0.2x^2 + 1.9x, which has
a = -0.2, b = 1.9.

The maximum height of the ball is
y_(v).

Then


\Delta = b^2-4ac = (1.9)^2 - 4*(-0.2)(0) = 3.61


y_(v) = -(3.61)/(4(-0.2)) = 4.5125

The highest height the ball achieves is 4.5125 meters.

User Ian Nato
by
8.3k points

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