Completing the Square Review

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, where p and q are constants.

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Take the coefficient of x (which is -4), divide it by 2 to get -2, and then square it to get 4. Add and subtract this value.

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

x = 1 and x = -7.

Divide it by 2 and square the result.

x = 6 and x = 2.

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

Set the squared term equal to the constant and solve for x by taking the square root of both sides.

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.