Solving Quadratics by completing the square

Front

Complete the square for x^2 + 6x + ____

Back

x^2 + 6x + 9

Front

Solve the quadratic equation by completing the square: x^2 - 10x - 5 = 0

Back

x = 5 ± √30

Front

Solve the equation by completing the square: x^2 + 4x - 5 = 11

Back

x = -2 ± √6

Front

Solve the equation by completing the square: x^2 + 6x - 4 = 36

Back

x = 4, -10

Front

Complete the square for x^2 + 12x + ____

Back

x^2 + 12x + 36

Front

What is the formula for completing the square?

Back

(x + b/2)^2 - (b/2)^2, where b is the coefficient of x.

Front

What does it mean to complete the square?

Back

To transform a quadratic equation into a perfect square trinomial.

Front

How do you find the vertex of a parabola from a completed square form?

Back

The vertex is at the point (-b/2, f(-b/2)) in the form y = a(x + b/2)^2 + k.

Front

What is the standard form of a quadratic equation?

Back

y = ax^2 + bx + c.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots.