Solving Quadratic Equations by Completing the Square

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to complete the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, making it easier to solve for x.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

How do you find the vertex of a parabola represented by a quadratic equation?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)) where f(x) is the quadratic function.

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 = x² + 2px + p².

Front

What is the formula for completing the square?

Back

To complete the square for ax² + bx, rewrite it as a(x² + (b/a)x) and then add (b/2a)² to both sides.

Front

Solve by completing the square: k² - 12k + 23 = 0

Back

k = 6 ± √13.

Front

What is the value of 'c' in the equation x² - 4x + c = 0 to make it a perfect square?

Back

c = 4.

Front

How do you convert a quadratic equation into vertex form?

Back

By completing the square, you can convert ax² + bx + c into a(x - h)² + k, where (h, k) is the vertex.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is given by b² - 4ac and determines the nature of the roots of the quadratic equation.