CPM Homework Help : A2C Problem 12-23

A cannon shoots a cannon ball into the air. The barrel of the cannon is located six feet above the ground. After two seconds the ball is $102$ feet above the ground. After four seconds it is $70$ feet above the ground. Find the equation of the parabola that models the path of the cannon ball.

Hint:

Identify the points that this information gives you.

Hint 2:

$\left(0, 6\right) \left(2, 102\right) \left(4, 70\right)$

Hint 3:

Use those points with the general equation of a parabola to create and solve a system of equations.

More Help:

$\left(6\right) = A\left(0\right)^{2} + B\left(0\right) + C\\\left(102\right) = A\left(2\right)^{2} + B\left(2\right) + C\\\left(70\right) = A\left(4\right)^{2} + B\left(4\right) + C$

Answer:

$h\left(t\right) = −16t^{2} + 80t + 6$