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 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 vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, found at the point (h, k) in the vertex form f(x) = a(x - h)² + k.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula h = -b/(2a) and k = f(h).

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, found by solving f(x) = 0.

Front

What does the 'a' value in a quadratic function determine?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What is completing the square?

Back

Completing the square is a method used to convert a quadratic equation into vertex form by adding and subtracting the same value.

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

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: D > 0 means two real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex; it is the y-coordinate of the vertex.