Complete the Square

Front

What is the first step in completing the square for a quadratic equation?

Back

Move the constant term to the other side of the equation.

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 standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0.

Front

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

Back

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

Front

What is the completed square form of the quadratic equation x² + 6x + 5?

Back

(x + 3)² - 4.

Front

How do you solve the equation x² + 4x - 5 = 0 by completing the square?

Back

(x + 2)² - 9 = 0, so x = -2 ± 3.

Front

What are the roots of the equation x² - 10x + 21 = 0 when solved by completing the square?

Back

x = 3 and x = 7.

Front

What is the relationship between the discriminant and the number of real roots?

Back

If the discriminant (b² - 4ac) is positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you simplify √800?

Back

20√2.

Front

What is the formula for the vertex of a parabola in standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h).