3.5 Vertex Form/Completing the Square

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you convert a quadratic function to vertex form?

Back

To convert a quadratic function to vertex form, you can complete the square on the quadratic expression.

Front

What is completing the square?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to analyze and graph.

Front

Given f(x) = ax² + bx + c, how do you find the vertex?

Back

The vertex can be found using the formula h = -b/(2a) and k = f(h).

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.

Front

Convert f(x) = 2x² + 8x + 3 to vertex form.

Back

f(x) = 2(x + 2)² - 5.

Front

Complete the square for x² + 6x + ____.

Back

x² + 6x + 9.

Front

What is the value needed to complete the square for x² - 10x?

Back

25.

Front

Convert f(x) = 3x² - 12x + 7 to vertex form.

Back

f(x) = 3(x - 2)² - 5.

Front

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

Back

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