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The given function for the height of the firework is a quadratic function
1. Time at which the firework reaches the maximum height is <u>1 seconds</u>
2. The maximum height of the firework, is <u>25 yards</u>
3. Time after which the firework will fall to the ground is<u> (1 + √5) seconds</u>
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Reason:
The given function that represents the height of the fireworks with time is
presented as follows;
h(t) = -5·t² + 10·t + 20
1. The time at which the firework reaches its maximum height is given by
the maximum point of the given function as follows;
The x-value of the maximum point of a quadratic function is
Where;
<em>a</em>, and <em>b</em>, are the coefficient of x² and <em>x</em>, in the general form of a quadratic function f(x) = a·x² + b·x + c
By comparison, we have;
- The time at which the firework reaches the maximum height is t = <u>1 seconds</u>
2. The maximum height is given by plugging in the value of <em>t</em>, at the maximum point into the given function as follows;
h(1) = -5×1² + 10×1 + 20 = 25
- The maximum height of the firework, f(1) = <u>25 yards</u>
3 The time at which the firework will fall to the ground, is given by the zero of the function as follows;
When the firework falls to the ground, h(t) = 0 = -5·t² + 10·t + 20
Dividing both sides by (-5) gives;
t² - 2·t - 4 = 0
By the quadratic formula , we get;
Therefore;
- The time after which the firework will fall to the ground, t = <u>1 + √5 seconds</u>
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