Vertex Form Flashcard

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does the 'a' value in the vertex form indicate about the parabola?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

How do you determine if a quadratic function has a maximum or minimum value?

Back

If the 'a' value in the vertex form is negative, the function has a maximum value. If 'a' is positive, the function has a minimum value.

Front

What transformations are represented by the vertex form of a quadratic function?

Back

The vertex form represents transformations such as vertical shifts (k), horizontal shifts (h), and reflections over the x-axis (if a < 0).

Front

How do you find the vertex of a quadratic function in vertex form?

Back

The vertex of the function f(x) = a(x - h)² + k is the point (h, k).

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts (or roots) are the values of x for which f(x) = 0. They can be found by solving the equation a(x - h)² + k = 0.

Front

How can you identify the x-intercepts from the vertex form of a quadratic function?

Back

Set the vertex form equal to zero and solve for x: a(x - h)² + k = 0.

Front

What does it mean to reflect a quadratic function over the x-axis?

Back

Reflecting a quadratic function over the x-axis means changing the sign of the 'a' value in the vertex form, which flips the parabola upside down.

Front

What is the significance of the 'h' value in the vertex form?

Back

The 'h' value represents the horizontal shift of the parabola. It indicates how far the graph is shifted left or right from the origin.

Front

What is the significance of the 'k' value in the vertex form?

Back

The 'k' value represents the vertical shift of the parabola. It indicates how far the graph is shifted up or down from the origin.