The quadratic equation that gives the height of the rocket, h = 156·t - 16·t² is evaluated at h = 60 feet to give the two times the rocket's height is 60 feet as 0.40 seconds and 9.35 seconds.
<h3>What is a quadratic equation?</h3>
A quadratic equation is an equation of the second degree that can be expressed in the form; a·x² + b·x + c = 0, where the letters, <em>a</em>, and <em>b </em>represents the coefficients of <em>x</em> and <em>c</em> is a constant.
The initial velocity of the rocket = 156 ft./s upwards
The given equation of the rocket is: h = 156·t - 16·t²
The times when the rocket height is 60 feet are found by plugging in the value <em>h </em> = 60, in the equation of the vertical height of the rocket as follows:
h = 60 = 156·t - 16·t²
156·t - 16·t² - 60 = 0
4·(39·t - 4·t² - 15) = 0
Therefore:
39·t - 4·t² - 15 = 0
-4·t² + 39·t - 15 = 0
From the quadratic formula which is used to solve the quadratic equation of the form; f(x) = a·x² + b·x + c, is presented as follows;
The solution of the equation, -4·t² + 39·t - 15 = 0, is therefore:
Therefore, when the height of the rocket is 60 feet, the times are: and
The times when the height of the rocket is 60 feet, the times are:
t ≈ 9.35 s, and <em>t </em>≈ 0.40 s
Learn more about quadratic equations in algebra here:
brainly.com/question/472337
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