Completing the Square 2/14

Front

What is the process to complete the square for a quadratic expression?

Back

1. Start with the quadratic expression in the form ax^2 + bx + c. 2. If a is not 1, factor it out. 3. Take the b value, divide it by 2, and square the result. 4. Add and subtract this square inside the expression. 5. Rewrite the expression as a perfect square trinomial.

Front

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

Back

Divide it by 2 and square the result.

Front

How do you complete the square for the expression x^2 - 10x + c?

Back

Add 25 to complete the square, resulting in x^2 - 10x + 25.

Front

What is the first step to solve the quadratic equation x^2 - 8x + 21 = 0 by completing the square?

Back

Subtract 21 from both sides.

Front

What value do you need to add to both sides to complete the square for x^2 - 12x + ... = 20 + ...?

Back

Add 36 to both sides.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as (x - a)^2 = x^2 - 2ax + a^2.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

How can you identify the vertex of a parabola from a completed square form?

Back

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

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation means rewriting it as a product of two binomials, such as (x - p)(x - q) = 0.