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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

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.

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 find the time at which the maximum height occurs, then substituting that time back into the height function.

Front

What is the formula for the discriminant of a quadratic equation?

Back

The discriminant is given by the formula D = b² - 4ac.

Front

What does the discriminant tell us about the roots of a quadratic equation?

Back

The discriminant indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root (a repeated root); if D < 0, there are no real roots.

Front

What is the maximum profit in a quadratic profit function?

Back

The maximum profit can be found at the vertex of the parabola represented by the profit function, using the formula x = -b/(2a) to find the price that maximizes profit.

Front

How do you determine the time it takes for an object to reach maximum height in projectile motion?

Back

Use the formula t = -b/(2a) from the height function h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

What is the significance of the initial velocity in projectile motion?

Back

The initial velocity determines how high and how far the object will travel before it starts to fall back down.

Front

What is the height of a projectile at time t = 0?

Back

The height at time t = 0 is given by the initial height h₀ in the height function.