SOLUTION: A grasshopper is perched on a reed 7 inches above the ground. It hops off the reed and lands on the ground about 11.7 inches away. During its hop, its height is given by the equa

Question 1053226: A grasshopper is perched on a reed 7 inches above the ground. It hops off the reed and lands on the ground about 11.7 inches away. During its hop, its height is given by the equation h= -0.2x^2+1.75x+7, where x is the distance in inches from the base of the reed, and h is in inches. How far was the grasshopper from the base of the reed when it was 4.25 inches above the ground? Round to the nearest tenth.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
h= -0.2x^2+1.75x+7. Graph it to get a sense of what is going on.

h(x)=4.25
4.25=-0.2x^2+1.75x+7
0=-0.2x^2+1.75x+2.75
x=-(1/0.4) (-1.75)-sqrt(3.0625-4(-0.2)(2.75)); sqrt term is 5.2625=2.37
x=-2.5*(-4.125)=10.3 cm
Note: here, you use the negative sqrt, since the leading coefficient is negative, 1/2a is negative as well. One can check by using the positive square root, and that will give rise to a negative x-value on the parabola. It is -1.55 cm, which is consistent with the graph.
One may bypass all of this by changing all the signs and treating it as a typical positive x^2 quadratic equation.
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