Solving Equations by Completing the Square

Front

What is the first step to solving a quadratic equation by completing the square?

Back

Isolate the constant term on one side of the equation.

Front

What is the formula for completing the square for the expression x^2 + bx?

Back

The completed square form is (x + b/2)^2 - (b/2)^2.

Front

How do you complete the square for the equation x^2 + 6x = 5?

Back

Add (6/2)^2 = 9 to both sides to get (x + 3)^2 = 14.

Front

What does it mean to complete the square?

Back

It means rewriting a quadratic expression in the form (x - p)^2 = q.

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.

Front

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

Back

Set the completed square expression equal to zero and solve for x.

Front

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

Back

The vertex x-coordinate is given by -b/(2a) from the standard form 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: two real, one real, or two complex.

Front

How do you factor a quadratic equation after completing the square?

Back

Rewrite the completed square form as a product of binomials.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax^2 + bx + c = 0.