5.1 Quadratic PF & Transformations

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the highest or lowest point of the graph, depending on whether it opens upwards or downwards.

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form y = ax² + bx + c.

Front

What is the effect of changing the value of 'a' in the quadratic function y = a(x-h)² + k?

Back

Changing the value of 'a' affects the width and direction of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does it mean if a parabola has a maximum value?

Back

A parabola has a maximum value if it opens downwards, indicating that the vertex is the highest point on the graph.

Front

What does it mean if a parabola has a minimum value?

Back

A parabola has a minimum value if it opens upwards, indicating that the vertex is the lowest point on the graph.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if 'a' is positive and downwards if 'a' is negative.

Front

What is the significance of the 'h' and 'k' in the vertex form of a quadratic function?

Back

In the vertex form y = a(x-h)² + k, 'h' represents the x-coordinate of the vertex and 'k' represents the y-coordinate of the vertex.

Front

What is the general shape of a quadratic function when graphed?

Back

Quadratic functions graph as a U-shaped curve called a parabola.