Determine the quadratic function whose graph is given.
-A coin is tossed upward from a balcony 320 ft high with an initial velocity of 32 ft/sec. During what interval of time will the coin be at a height of at least 80 ft? (h = -16t² + vot + ho.)

Question

Quizplus · Accepted Answer

The quadratic function for the height of the coin at time $t$ is given by $h(t) = -16t^2 + 32t + 320$. To find when the coin is at least 80 ft high, we set $h(t) \geq 80$ and solve for $t$. Substituting $h(t) = 80$ into the equation gives us $-16t^2 + 32t + 320 = 80$. Simplifying, we get $-16t^2 + 32t + 240 = 0$. Factoring or using the quadratic formula, we find the values of $t$ that satisfy this equation. The interval $0 \leq t \leq 5$ includes the times when the coin is launched until it reaches the ground again, considering the initial height and velocity.

Determine the Quadratic Function Whose Graph Is Given