Question

4. A field mouse hops along a parabolic path given by y=-0.2x^2+1.3x where x is the mouse's horizontal position (in feet) and y is the corresponding height (in feet).

Answer 1

Given that A field mouse hops along a parabolic path given by

`y=-0.2x^2+1.3x`

To find how far does the mouse jump, substitute with y = 0 and solve for x

so,

`\begin{gathered} y=0 \\ -0.2x^2+1.3x=0 \\ x(-0.2x+1.3)=0 \\ x=0 \\ -0.2x+1.3=0\rightarrow x=(1.3)/(0.2)=6.5 \end{gathered}`

So, the midpoint of the parabola will be:

`x_m=(6.5)/(2)=3.25`

so, substitute with the last value to find the highest point:

`y=-0.2\cdot3.25^2+1.3\cdot3.25=2.1125`

so, the answer will be y = 2.1125

This means the mouse can jump to 2.1125 feet

Also, the highest value of the bath will be 6.5 feet

Part B:

Can the mouse jump over 3 feet?

As the highest point is 2.1125 feet, the mouse can not jump over 3 feet.