The height of water shooting from a fountain is modeled by the function f(x) = −4x2 + 24x − 29 where x is the distance from the spout in feet. Complete the square to determine the maximum height of the path of the water. −4(x − 3)2 − 29; The maximum height of the water is 3 feet. −4(x − 3)2 − 29; The maximum height of the water is 29 feet. −4(x − 3)2 + 7; The maximum height of the water is 7 feet. −4(x − 3)2 + 7; The maximum height of the water is 3 feet.

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The height of water shooting from a fountain is modeled by the function f(x) = −4x2 + 24x − 29 where x is the distance from the spout in feet. Complete the square to determine the maximum height of the path of the water. −4(x − 3)2 − 29; The maximum height of the water is 3 feet. −4(x − 3)2 − 29; The maximum height of the water is 29 feet. −4(x − 3)2 + 7; The maximum height of the water is 7 feet. −4(x − 3)2 + 7; The maximum height of the water is 3 feet.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Use the complete the square formula. \[{a(x+D)}^{2}+E\] −4x^2 + 24x − 29 is ax^2 + bx + c. a = -4, b = 24, and c = -29. Find D. \[D=\frac{b}{2a}=\frac{24}{2\times -4}\] Then, find E. \[E=c-\frac{{b}^{2}}{4a}=-29-\frac{{24}^{2}}{4\times -4}\] Once you've found D and E, plug them into the complete the square formula. \[{a(x+D)}^{2}+E\]
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