Question 233345
Let the fence be at x = 0.


Rabbit has to start jump at x = -4 and end jump at x = 4


Rabbit jump will be in the form of a parabola that opens downward and peaks at x = 0.


Parabola that opens down and peaks up needs the a term to be equal to 0.


Quadratic equation models a parabole.


standard form of a quadratic equation is ax^2 + bx + c = 0


Roots have to be x = -4 and x = + 4


Equation would have to be of the form:


(x-4)*(x+4) = 0


Multiply (x-4)*(x_4) to get x^2 - 16 = 0


Multiply that by -1 to get:


-x^2 + 16 = 0


That allows the equation to peak at x = 0 and still cross at x = -4 and x = 4.


Equation will look like the following:


{{{graph(400,400,-5,5,-10,30,-x^2 + 16)}}}