SOLUTION: A football is kicked into the air and follows the path defined by h=-2x^2+16x, where x is the time in seconds and h is the height in metres.What is the maximum height reached by th
Question 120774: A football is kicked into the air and follows the path defined by h=-2x^2+16x, where x is the time in seconds and h is the height in metres.What is the maximum height reached by the football? Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! If you are familiar with the quadratic formula, then you know that a quadratic equation of
the generic standard form:
.
.
has as its solutions for x the values that are given by:
.
.
The first term on the right side specifies the axis of symmetry. In other words, the axis
of symmetry is given by:
.
.
{Now to your problem. First recognize that the highest point in the parabolic path of the
football will occur along the axis of symmetry. So let's first find the axis of symmetry
.
Let h be zero so that your quadratic equation of:
.
.
becomes:
. which, by switching sides further becomes
.
Comparing this term by term to the generic quadratic standard form you can see that a = -2,
b = +16, and c = 0. Now you can go to the equation for the axis of symmetry to find the
value of x for the axis of symmetry by substituting -2 for a and +16 for b to get that
the equation for the axis of symmetry is:
.
.
This tells you that the axis of symmetry is the vertical line through the point on the x-axis
where x = +4. So you can tell that the peak in the flight of the ball will occur when
x = 4 seconds.
.
Return to your equation for the height of the football and you can find the peak height of
the ball by substituting 4 for x as follows:
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This tells you that the maximum height of the football is 32 metres.
.
Hope this helps you to understand one way that this problem can be solved.
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