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 whether it opens up or down.

Front

What does it mean if a quadratic function opens upwards?

Back

It means the parabola has a minimum value at its vertex.

Front

What does it mean if a quadratic function opens downwards?

Back

It means the parabola has a maximum value at its vertex.

Front

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

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)) from the function f(x) = ax^2 + bx + c.

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 is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two mirror-image halves.

Front

How can you identify the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value is the y-coordinate of the vertex.

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 effect 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 its width.