Completing the Square

Front

What is the process of completing the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, where p and q are constants. This is done by manipulating the equation to form a perfect square trinomial.

Front

How do you find the value of 'c' to complete the square for the expression x² + bx + c?

Back

To find 'c', take half of the coefficient of x (which is b), square it, and add it to the expression. Thus, c = (b/2)².

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x - p)² or (x + p)².

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 solve a quadratic equation by completing the square?

Back

1. Move the constant term to the other side of the equation. 2. Complete the square on the left side. 3. Take the square root of both sides. 4. Solve for x.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

How can you identify a perfect square trinomial from a quadratic expression?

Back

A quadratic expression is a perfect square trinomial if the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens (upward or downward).

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert, complete the square on the quadratic expression and rewrite it in the form y = a(x - h)² + k.