Understanding Graphs of Quadratic Functions

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the vertex of the function f(x) = a(x-h)² + k?

Back

The vertex is the point (h, k).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola.

Front

How do you determine the axis of symmetry from the vertex form of a quadratic function?

Back

The axis of symmetry is x = h, where (h, k) is the vertex.

Front

What are x-intercepts in a quadratic function?

Back

X-intercepts are the points where the graph crosses the x-axis, found by setting f(x) = 0.

Front

How do you find the x-intercepts of the function f(x) = ax² + bx + c?

Back

Use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the range of a quadratic function that opens upwards?

Back

The range is all real numbers greater than or equal to the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is all real numbers less than or equal to the y-coordinate of the vertex.

Front

What does the term 'parabola' refer to in mathematics?

Back

A parabola is the graph of a quadratic function, shaped like a U or an upside-down U.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c.