Alg 2 Quadratic Applications

Front

What is a quadratic function?

Back

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

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola (upward or downward).

Front

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

Back

The maximum height can be found using the vertex formula t = -b/(2a) for the time at which the maximum occurs, then substituting this value back into the height equation.

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

How do you determine the initial height of an object from its quadratic height equation?

Back

The initial height is the constant term (c) in the quadratic equation when t = 0.

Front

What is the formula to find the time when an object hits the ground in a quadratic height equation?

Back

Set the height equation equal to zero (h(t) = 0) and solve for t.

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation: if D > 0, there are two real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How can you find the time of flight for an object modeled by a quadratic function?

Back

The time of flight is found by solving the quadratic equation for when the height is zero (h(t) = 0).

Front

What is the formula for the height of an object in free fall?

Back

The height of an object in free fall can be modeled by the equation h(t) = -16t² + v₀t + h₀, where v₀ is the initial velocity and h₀ is the initial height.

Front

What does the term 'maximum height' mean in the context of projectile motion?

Back

Maximum height refers to the highest point reached by the object during its flight before it starts descending.