Completing the Square

Front

What is completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting them in the form (x + p)² = q, making it easier to find the roots.

Front

What is the formula to complete the square for the expression x² + bx?

Back

To complete the square, add (b/2)² to both sides of the equation.

Front

What do you add to both sides of the equation x² + 12x = 5 to complete the square?

Back

36

Front

What is the first step to solving the equation a² + 10a + 21 = 0 by completing the square?

Back

Subtract 21 from both sides.

Front

What value completes the square for the expression x² + 16x + _?

Back

64

Front

When do you use the plus or minus symbol (±) in completing the square?

Back

After taking the square root of both sides.

Front

Complete the square for the expression x² + 6x + ___.

Back

9

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 vertex of a parabola given in standard form?

Back

The vertex can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

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.