Quadratic Word Problems

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found at the vertex, which occurs at x = -b/(2a).

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward or downward) and affects the width of the parabola.

Front

What is the formula for the height of an object in projectile motion?

Back

The height h(t) of an object in projectile motion can be modeled by the equation h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

What does the term 'initial velocity' mean in the context of projectile motion?

Back

Initial velocity is the speed at which an object is launched or thrown at the beginning of its motion.

Front

What is the role of gravity in projectile motion?

Back

Gravity accelerates the object downwards at a rate of approximately 32 ft/s², which is represented by the -16t² term in the height equation.

Front

How do you determine the time it takes for an object to reach a certain height?

Back

To find the time, set the height equation equal to the desired height and solve for t.

Front

What is the maximum height of a projectile?

Back

The maximum height can be found by calculating the vertex of the quadratic equation representing the height.