Quadratic Functions in Vertex Form

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you identify the vertex from the vertex form equation?

Back

In the equation y = a(x - h)² + k, the vertex is the point (h, k).

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 its width (larger |a| means narrower, smaller |a| means wider).

Front

Given the equation y = 2(x + 3)² + 4, what is the vertex?

Back

The vertex is (-3, 4).

Front

What is the effect of changing the 'h' value in the vertex form?

Back

Changing the 'h' value shifts the parabola left or right along the x-axis.

Front

What is the effect of changing the 'k' value in the vertex form?

Back

Changing the 'k' value shifts the parabola up or down along the y-axis.

Front

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

Back

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

Front

What is the vertex of the function f(x) = -(x - 2)² - 1?

Back

The vertex is (2, -1).

Front

How do you convert the standard form of a quadratic equation to vertex form?

Back

To convert, complete the square on the quadratic expression.

Front

What is the vertex of the function y = 3(x + 1)² - 5?

Back

The vertex is (-1, -5).