Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the vertex of a parabola given in standard form?

Back

To find the vertex of a parabola in standard form f(x) = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

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 = h, where (h, k) is the vertex.

Front

What does it mean to complete the square?

Back

Completing the square is a method used to convert a quadratic expression into a perfect square trinomial, making it easier to analyze and graph.

Front

How do you convert a quadratic function from standard form to vertex form?

Back

To convert from standard form f(x) = ax² + bx + c to vertex form, complete the square on the quadratic expression.

Front

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

Back

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

Front

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

Back

The maximum or minimum value occurs at the vertex of the parabola. If a > 0, the vertex is a minimum; if a < 0, the vertex is a maximum.

Front

How do you determine the intervals of increase and decrease for a quadratic function?

Back

A quadratic function increases on the interval to the right of the vertex and decreases on the interval to the left of the vertex.

Front

What is the formula for the vertex of a parabola given by the equation y = ax² + bx + c?

Back

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