Quadratic Word Problem Practice

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 (opening upwards or downwards).

Front

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

Back

The maximum height can be found using the formula t = -b/(2a) to determine the time at which the maximum height occurs, then substituting that time back into the height function.

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 when a projectile hits the ground using a quadratic function?

Back

Set the height function equal to zero and solve for t to find the time when the projectile reaches the ground.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How can you find the height of a projectile at a specific time?

Back

Substitute the specific time value into the height function h(t) to calculate the height at that time.

Front

What is the initial height in a projectile motion equation?

Back

The initial height is the constant term (c) in the height function, representing the height from which the projectile is launched.