Completing the Square

Front

What is the process of completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, where p and q are constants.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you find the value to complete the square for the equation x² + bx?

Back

To complete the square, take the coefficient b, divide it by 2, and square the result.

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

Solve by completing the square: n² - 2n - 3 = 0

Back

n = 3 and n = -1.

Front

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

Back

y = -1 and y = -9.

Front

Solve by completing the square: k² - 12k + 23 = 0

Back

k = 6 + √13 and k = 6 - √13.

Front

Solve by completing the square: x² + 12x = 5

Back

x = -6 + √41 and x = -6 - √41.

Front

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

Back

Divide it by 2 and square the result.

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.