Applications with Quadratics

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 is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a) for the quadratic function ax² + bx + c.

Front

How do you find the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found by determining the vertex of the parabola, which occurs at t = -b/(2a) in the function h(t) = -16t² + bt + c.

Front

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

Back

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

Front

What is the initial height in a projectile motion equation?

Back

The initial height is the value of the function when t = 0, represented by the constant term c in the quadratic equation.

Front

How do you calculate the height of a projectile at a specific time?

Back

To calculate the height at a specific time, substitute the value of t into the quadratic function h(t) = -16t² + bt + c.

Front

What is the formula for the height of a projectile launched from a height?

Back

The height of a projectile launched from a height is modeled by h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

What does the term 'projectile motion' refer to?

Back

Projectile motion refers to the motion of an object that is thrown or projected into the air, subject to the force of gravity.

Front

How do you determine the time it takes for a projectile to reach its maximum height?

Back

The time to reach maximum height is found using t = -b/(2a) from the quadratic equation h(t) = -16t² + bt + c.