Practice Flashcard Applications of Quadratic Functions

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 x-intercepts of a quadratic function?

Back

To find the x-intercepts, set the quadratic function equal to zero and solve for x using factoring, completing the square, or 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 ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is the significance of the leading coefficient in a quadratic function?

Back

The leading coefficient (a) 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 maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found at the vertex, calculated using the formula y = f(-b/(2a)).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

How do you interpret the profit function P = 2x² - 44x - 150?

Back

This function models profit based on the number of meals catered (x). The profit is positive when P > 0, indicating a profit, and negative when P < 0, indicating a loss.

Front

What is the initial height in a projectile motion equation?

Back

The initial height is the value of h when t = 0, representing the starting height of the object before it begins to move.