Quadratic Word Problems

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 vertex formula t = -b/(2a), where a and b are coefficients from the quadratic equation h(t) = at² + bt + c.

Front

What is the significance of the 'h' in the height function h(t)?

Back

In the context of projectile motion, 'h' represents the height of the object above the ground at time 't'.

Front

What does the term 'initial height' refer to in projectile motion?

Back

The initial height is the height from which the object is launched or thrown, represented by the constant term in the quadratic equation.

Front

How can you determine when an object hits the ground using a quadratic function?

Back

An object hits the ground when its height h(t) = 0. You can find this by solving the quadratic equation for t.

Front

What is the formula to calculate the time it takes for an object to reach its maximum height?

Back

The time to reach maximum height is given by t = -b/(2a), where a and b are the coefficients from the quadratic equation.

Front

What does the coefficient 'a' indicate in a quadratic function?

Back

The coefficient 'a' indicates the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

How do you interpret the roots of a quadratic equation in the context of projectile motion?

Back

The roots of a quadratic equation represent the times at which the projectile is at ground level (h = 0).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is f(x) = ax² + bx + c.