A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base...

Question:

A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the linger base to be 7 yards greater than the height. She wants the area to be 295 square yards. The situation is molded by the equation {eq}h^2+5h=295 {/eq}. Use the quadratic formula to find the height that will give the desired area. Round to the nearest hundredth of a yard.

The quadratic formula

When we are unable to factorize a quadratic with integer factors, we often need to use the quadratic formula to solve. The quadratic formula takes the coefficients A, B and C and returns the solutions to x. {eq}x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\ {/eq}

Answer and Explanation:

Our quadratic equation is {eq}h^2 + 5h = 295 \\ h^2 + 5h - 295 = 0 \\ {/eq} Therefore, a is 1, b is 5 and c is -295. We can then substitute these values into the equation. {eq}h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\ h = \frac{-5 \pm \sqrt{5^2 - 4(1)(-295)}}{2(1)} \\ h = \frac{-5 \pm \sqrt{5^2 - 4(1)(-295)}}{2} \\ h = \frac{-5 \pm \sqrt{1205}}{2} \\ h = \frac{-5 \pm 34.7}{2} \\ h = \frac{-5 + 34.7}{2} \text{ and } h = \frac{-5 - 34.7}{2} \\ h = \frac{ 29.7}{2} \text{ and } h = \frac{-39.7}{2} \\ h = 14.86 \text{ and } h = - 19.86 \\ {/eq} Since we know height cannot be negative, the height equals 14.86 yards to the nearest hundredth.


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How to Use the Quadratic Formula to Solve a Quadratic Equation

from Math 101: College Algebra

Chapter 4 / Lesson 10
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