Solve the problem. Round your answer to the nearest tenth, when appropriate.
-A grasshopper is perched on a reed 6 inches above the ground. It hops off the reed and lands on the ground about 10.4 inches away. During its hop, its height is given by the equation $h=-0.2 x^{2}+1.50 x+6$, 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 3.25 inches above the ground?
A) 1.5 in.
B) 9.0 in.
C) 3.2 in.
D) 10.4 in.

Question

Quizplus · Accepted Answer

To find the distance $x$ when the grasshopper was 3.25 inches above the ground, we substitute $h = 3.25$ into the equation and solve for $x$:$$3.25 = -0.2x^2 + 1.50x + 6.$$Rearranging gives:$$0 = -0.2x^2 + 1.50x + 2.75.$$Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = -0.2$, $b = 1.5$, and $c = 2.75$, we find the values of $x$ that satisfy the equation. The positive value close to 9 inches is the relevant solution since it represents the distance from the base of the reed to where the grasshopper lands, matching the context of the problem.

Solve the Problem h=−0.2x2+1.50x+6h=-0.2 x^{2}+1.50 x+6h=−0.2x2+1.50x+6 , Where xxx Is the Distance in Inches from the Base of the When

Solve the Problem $h=-0.2 x^{2}+1.50 x+6$ , Where $x$ Is the Distance in Inches from the Base of the When