Quadratic Word Problems

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, 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.

Front

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

Back

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

Front

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

Back

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

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the formula to find the roots of a quadratic equation?

Back

The roots can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

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 determine when an object reaches the ground using a quadratic equation?

Back

Set the height equation equal to zero and solve for t to find when the object is at ground level.

Front

What is the maximum profit in a quadratic profit function?

Back

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

Front

What does the 'c' value represent in a quadratic equation?

Back

The 'c' value represents the y-intercept of the quadratic function, which is the height of the object at time t = 0.