Completing The Square Practice

Front

What is the process of 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 solve or analyze.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression of the form (a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b².

Front

How do you complete the square for the equation x² + 6x = 5?

Back

Add (6/2)² = 9 to both sides: x² + 6x + 9 = 14, which factors to (x + 3)² = 14.

Front

What value of 'c' completes the square in x² + 8x + c?

Back

c = (8/2)² = 16.

Front

Solve the equation x² + 12x + 36 = 0 by completing the square.

Back

(x + 6)² = 0, so x = -6.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you find the roots of a quadratic equation using completing the square?

Back

Rearrange the equation to the form x² + bx = c, complete the square, and then solve for x.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

Complete the square for the equation x² + 4x = 8.

Back

Add (4/2)² = 4 to both sides: (x + 2)² = 12.

Front

What is the first step in completing the square for x² + 10x + 5 = 0?

Back

Move the constant term to the other side: x² + 10x = -5.