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 (upward or downward).

Front

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

Back

To find the maximum height, use the formula t = -b/(2a) to find the time at which the maximum occurs, then substitute this time back into the height equation.

Front

What is the standard form of a quadratic equation?

Back

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

Front

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

Back

The 'a' value determines the direction of the parabola: if a > 0, the parabola opens upward; if a < 0, it opens downward.

Front

How can you determine the time it takes for an object to reach a certain height using a quadratic equation?

Back

Set the height equation equal to the desired height and solve for t using the quadratic formula.

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 you?

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 do you interpret the coefficients in a profit function modeled by a quadratic equation?

Back

In a profit function p = ax² + bx + c, 'a' indicates the rate of change of profit, 'b' indicates the linear contribution, and 'c' represents fixed costs or initial profit.

Front

What is the maximum profit in a quadratic profit function?

Back

The maximum profit occurs at the vertex of the parabola, which can be found using t = -b/(2a) in the profit equation.