Vertex Form

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is given by: f(x) = 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?

Back

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

Front

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

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

Convert the standard form of a quadratic equation to vertex form: y = x² + 4x + 1.

Back

To convert, complete the square: y = (x + 2)² - 3, so the vertex form is f(x) = (x + 2)² - 3.

Front

What is the vertex of the equation y = 2(x - 3)² + 4?

Back

The vertex is (3, 4).

Front

How do you find the x-coordinate of the vertex from the vertex form?

Back

The x-coordinate of the vertex is found from the equation f(x) = a(x - h)² + k, where h is the x-coordinate.

Front

If a quadratic function opens downwards, what can you say about the 'a' value?

Back

If a quadratic function opens downwards, the 'a' value is negative.

Front

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

Back

Changing the 'k' value shifts the graph vertically: increasing 'k' moves the graph up, while decreasing 'k' moves it down.

Front

Identify the vertex of the function f(x) = -3(x + 1)² + 2.

Back

The vertex is (-1, 2).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.