Completing the Square Problems

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 do you need to add to both sides to complete the square for the expression x² - 12x?

Back

Add 36 to both sides.

Front

When factoring x² - 4x + 4 = 20, what goes in the blank? (x - __ )² = 20

Back

2

Front

What do you do to the b value to correctly complete the square?

Back

Divide it by 2 and square the result.

Front

Solve by completing the square: y² + 10y = -9

Back

y = -1 and y = -9.

Front

What is the formula for completing the square for a quadratic equation ax² + bx + c?

Back

(x + b/2a)² - (b² - 4ac)/4a.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you find the vertex of a parabola given in standard form?

Back

Use the formula h = -b/(2a) to find the x-coordinate.

Front

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

Back

It determines the nature of the roots: positive (two real roots), zero (one real root), negative (no real roots).

Front

What is the relationship between the coefficients and the roots of a quadratic equation?

Back

The sum of the roots is -b/a and the product is c/a.