Super Bowl Algebra Challenge

The path of a quarterback's pass by the Kansas City Chiefs can be modeled by the equation $h(t) = -16t^2 + 48t + 4$ where $h$ is the height in feet. What is the maximum height of the pass?

Describe how the equation $h(t) = -16t^2 + 35t + 6$ models the height of a kicked football by the Tampa Bay Buccaneers during a Super Bowl game. Include the factors that affect its path.

If a ball is kicked with an initial velocity of 35 ft/s, write the height equation $h(t)$ assuming the initial height is 3 feet.

A running back from the Green Bay Packers' average yards per play can be modeled by the function $f(x) = -2x^2 + 10x + 15$. What do the x-intercepts represent?

If the function $f(x) = 3x^2 - 24x + 36$ models the New England Patriots' score fluctuation, what does the vertex of the function represent in the context of a game?

The parabola for a touchdown pass by the San Francisco 49ers will always open downwards when modeled with $-16x^2$ as the leading coefficient.

Using the polynomial $p(x) = x^3 - 2x^2 - 5x + 6$, describe how this represents changes in the score of the Dallas Cowboys over time in a Super Bowl game.

Calculate the score change represented by the polynomial $p(x) = 2x^2 - 3x + 5$ at $x = 4$.

Given the polynomial $2x^3 - 9x^2 + 7x - 5$, which value represents the leading coefficient when modeling a Super Bowl game's scoring trend for the Pittsburgh Steelers?

If the Los Angeles Rams scored $f(t) = 3t + 7$ and the New York Giants scored $g(t) = 5t - 4$, for which $t$ do the Rams catch up to the Giants?

In a Super Bowl, using a quadratic to model the trajectory of a thrown ball by the Miami Dolphins assumes air friction is negligible.

The polynomial $s(x) = x^2 - x - 20$ models a Super Bowl game’s point trends for the Chicago Bears. Which values of $x$ make the score zero?