Given that A field mouse hops along a parabolic path given by
[tex]y=-0.2x^2+1.3x[/tex]
To find how far does the mouse jump, substitute with y = 0 and solve for x
so,
[tex]\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=\frac{1.3}{0.2}=6.5 \end{gathered}[/tex]
So, the midpoint of the parabola will be:
[tex]x_m=\frac{6.5}{2}=3.25[/tex]
so, substitute with the last value to find the highest point:
[tex]y=-0.2\cdot3.25^2+1.3\cdot3.25=2.1125[/tex]
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.
