Question

When changing a standard form equation into vertex form, what is the process called where a number is added and subtracted to complete the square?

A) Vertex transformation
B) Quadratic adjustment
C) Completing the square
D) Factorization

Answer 1

The process where a number is added and subtracted in a quadratic equation to complete the square is called Completing the square, which is used to convert the equation to vertex form.

Step-by-step explanation:

When changing a standard form equation into vertex form, the process where a number is added and subtracted to complete the square is called Completing the square. This algebraic technique is used to transform a quadratic equation of the form ax^2 + bx + c = 0 into the vertex form a(x-h)^2 + k where (h, k) is the vertex of the parabola represented by the equation.

To complete the square, one typically takes the following steps:

1. Divide the quadratic and linear coefficients by a, if a ≠ 1.
2. Add and subtract the square of half the coefficient of x inside the parentheses.
3. Rearrange the equation to isolate the completed square and the constant terms.

This method is often used as an alternative to the quadratic formula for finding the roots of a quadratic equation or for graphing purposes.