Using the vertex of a <em>quadratic equation</em>, it is found that:
- The <u>maximum height</u> using Max Jumps is of 16 inches.
- The <u>maximum height</u> using Jumpsters is of 38 inches.
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Suppose we have a <u>concave-down</u> quadratic equation given by:
![y = ax^2 + bx + c, a < 0](https://tex.z-dn.net/?f=y%20%3D%20ax%5E2%20%2B%20bx%20%2B%20c%2C%20a%20%3C%200)
The maximum value is given by:
![y_V = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}](https://tex.z-dn.net/?f=y_V%20%3D%20-%5Cfrac%7B%5CDelta%7D%7B4a%7D%20%3D%20-%5Cfrac%7Bb%5E2%20-%204ac%7D%7B4a%7D)
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The equation for the height of Max Jumps is:
![f(x) = -192(x - 0.289^2) + 16](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-192%28x%20-%200.289%5E2%29%20%2B%2016)
Putting it into standard form:
![f(x) = -192x^2 + 110.976x - 0.036032 ](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-192x%5E2%20%2B%20110.976x%20-%200.036032%0A)
Thus, the coefficients are
, and the maximum height is of:
![y_V = -\frac{b^2 - 4ac}{4a} = -\frac{(110.976)^2 - 4(-192)(-0.036032)}{4(-192)} = 16](https://tex.z-dn.net/?f=y_V%20%3D%20-%5Cfrac%7Bb%5E2%20-%204ac%7D%7B4a%7D%20%3D%20-%5Cfrac%7B%28110.976%29%5E2%20-%204%28-192%29%28-0.036032%29%7D%7B4%28-192%29%7D%20%3D%2016)
Maximum height of 16 inches.
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The equation for the height of Jumpsters is:
![f(x) = -192(x - 0.445^2) + 38](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-192%28x%20-%200.445%5E2%29%20%2B%2038)
Putting it into standard form:
![f(x) = -192x^2 + 170.88x - 0.0208](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-192x%5E2%20%2B%20170.88x%20-%200.0208)
Thus, the coefficients are
, and the maximum height is of:
![y_V = -\frac{b^2 - 4ac}{4a} = -\frac{(170.88)^2 - 4(-192)(-0.0208)}{4(-192)} = 38](https://tex.z-dn.net/?f=y_V%20%3D%20-%5Cfrac%7Bb%5E2%20-%204ac%7D%7B4a%7D%20%3D%20-%5Cfrac%7B%28170.88%29%5E2%20-%204%28-192%29%28-0.0208%29%7D%7B4%28-192%29%7D%20%3D%2038)
Maximum height of 38 inches.
A similar problem is given at brainly.com/question/16858635