Key Characteristics of Quadratics: Flashcard Review

Front

What is the vertex of the quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. For example, in the function y = a(x-h)^2 + k, the vertex is (h, k).

Front

What is the axis of symmetry of a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a) for a quadratic in the form y = ax^2 + bx + c.

Front

What is the graph of a quadratic function called?

Back

The graph of a quadratic function is called a parabola.

Front

What is the range of the quadratic function y = ax^2 + bx + c when a > 0?

Back

The range is y >= k, where k is the y-coordinate of the vertex, which is the minimum point.

Front

What is the range of the quadratic function y = ax^2 + bx + c when a < 0?

Back

The range is y <= k, where k is the y-coordinate of the vertex, which is the maximum point.

Front

When a parabola opens downward, what is the nature of the vertex?

Back

The vertex is a maximum point.

Front

When a parabola opens upward, what is the nature of the vertex?

Back

The vertex is a minimum point.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax^2 + bx + c, where a, b, and c are constants.

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 the effect of changing the 'b' value in a quadratic function?

Back

The 'b' value affects the position of the vertex along the x-axis and the axis of symmetry.