Graphs of Quadratics and Their Characteristics

Front

What is the shape of the graph of a quadratic function?

Back

The graph of a quadratic function is called a parabola.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the graph of a parabola.

Front

What does it mean for a function to be increasing?

Back

A function is increasing when its output values rise as the input values increase.

Front

What is the range of a quadratic function with a maximum vertex?

Back

The range is the set of all output values, typically expressed as (-∞, k] where k is the maximum value.

Front

What is the range of a quadratic function with a minimum vertex?

Back

The range is the set of all output values, typically expressed as [k, ∞) where k is the minimum value.

Front

What are the roots of a quadratic function?

Back

The roots are the x-values where the graph intersects the x-axis, also known as zeros.

Front

How do you determine if a parabola opens upwards or downwards?

Back

A parabola opens upwards if the coefficient of the x^2 term is positive and downwards if it is negative.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is f(x) = a(x-h)^2 + k, where (h, k) is the vertex.