Complete the Square Practice

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

To convert from standard form y = ax² + bx + c to vertex form, complete the square.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic in the form x² + bx as (x + b/2)² - (b/2)².

Front

What is the vertex of the parabola represented by the equation y = 2(x - 3)² + 5?

Back

The vertex is (3, 5).

Front

Given the equation y = x² - 6x + 8, what is the vertex form?

Back

The vertex form is y = (x - 3)² - 1.

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

How do you find the value to complete the square for x² + 10x + ____?

Back

Take half of 10 (which is 5), square it (25), and add it to the equation: x² + 10x + 25.

Front

What is the completed square form of x² - 8x?

Back

The completed square form is (x - 4)² - 16.

Front

If a quadratic opens upwards, what can you say about its vertex?

Back

The vertex is the minimum point of the parabola.

Front

If a quadratic opens downwards, what can you say about its vertex?

Back

The vertex is the maximum point of the parabola.