document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #668512 by Boreal(15235) $\"\"$ $\"About$

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h= -0.2x^2+1.75x+7. Graph it to get a sense of what is going on.
\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C12%2C-10%2C12%2C-0.2x%5E2%2B1.75x%2B7%29\"$
\n" ); document.write( "h(x)=4.25
\n" ); document.write( "4.25=-0.2x^2+1.75x+7
\n" ); document.write( "0=-0.2x^2+1.75x+2.75
\n" ); document.write( "x=-(1/0.4) (-1.75)-sqrt(3.0625-4(-0.2)(2.75)); sqrt term is 5.2625=2.37
\n" ); document.write( "x=-2.5*(-4.125)=10.3 cm
\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "One may bypass all of this by changing all the signs and treating it as a typical positive x^2 quadratic equation. \n" ); document.write( "

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