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ra1l [238]
2 years ago
13

Help plz!! The function h(t)=-16t^2+22t+4 models the height (h) of a football t seconds after it is thrown. The question ask to

the nearest foot, what is the greatest height that the football reaches? (Little help: Function in vertex form is h(t)=-16(x-11/16)^2+185/16)
Mathematics
1 answer:
Black_prince [1.1K]2 years ago
8 0
If you're familiar with the quadratic equation
\frac{ -b \pm \sqrt{b^2-4ac}}{2a}

well, \frac{ -b}{2a} is the x component of the vertex, in your case, the vertex is the highest point

figure out what t is at the highest point, and then substitute that back into the equation in order to determine height

x=t in this problem
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Use Euclide's formula for generating Pythagorean triples.

This formula states that given two arbitrary different integers, x and y, both greater than zero, then the following numbers a, b, c form a Pythagorean triple:

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From a = x^2 - y^2, you need that x > y, then you can discard options A and D.

Now you have to probe the other options.

Start with option B, x = 4, y = 3

a = x^2 - y^2 = 4^2 - 3^2 = 16 -9 = 7

b = 2xy = 2(4)(3) = 24

c = x^2 9 y^2  = 4^2 + 3^2 = 16 + 9 = 25

Then we could generate the Pythagorean triple (7, 24, 25) with x = 4 and y =3.

If you want, you can check that a^2 + b^2 = c^2; i.e. 7^2 + 24^2 = 25^2

The answer is the option B. x = 4, y = 3
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