Completing the Square Review

Front

What is the process of completing 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, where p and q are constants.

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 find the value to complete the square for the expression x² - 4x?

Back

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.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

Solve by completing the square: x² + 6x = 7

Back

x = 1 and x = -7.

Front

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

Back

Divide it by 2 and square the result.

Front

Solve by completing the square: x² - 8x + 12 = 0

Back

x = 6 and x = 2.

Front

What is the first step in completing the square for the equation x² + 10x = -9?

Back

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

Front

How do you determine the roots of a quadratic equation after completing the square?

Back

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

Front

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

Back

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.