Completing the Square: Quadratic Equations

What is the first step in completing the square for a quadratic equation?

• Add a constant to both sides

• Divide the equation by the coefficient of x

• Move the constant to the other side

• Multiply both sides by a constant

In the simple quadratic example, what is the value added to both sides to complete the square?

• 5

• 4

• 3

• 2

What is the vertex form of the quadratic equation after completing the square in the simple example?

• y = (x + 2)² - 1

• y = (x - 2)² + 1

• y = (x + 1)² - 2

• y = (x - 1)² + 2

When completing the square for a quadratic with a coefficient, what should you do with the coefficient?

• Multiply it by the constant

• Add it to both sides

• Factor it out

• Ignore it

In the quadratic with a coefficient example, what is the vertex of the equation?

• (-2, -13)

• (2, 13)

• (2, -13)

• (-2, 13)

What makes the last example more challenging?

• It includes a fraction and a negative

• It has a larger constant

• It involves a higher degree polynomial

• It requires a different method

In the complex example, what is the reciprocal used for when factoring out the negative fraction?

• To divide the constant

• To add to both sides

• To simplify the equation

• To multiply inside the parenthesis

What is the final vertex form of the quadratic in the complex example?

• y = -1/4(x + 4)² + 9

• y = 1/4(x - 4)² - 9

• y = -1/4(x - 4)² + 9

• y = 1/4(x + 4)² - 9

What does a negative 'a' value indicate about the graph of the quadratic?

• It opens upwards

• It opens downwards

• It is a vertical line

• It is a horizontal line

How does the 1/4 coefficient affect the graph of the quadratic?

• It shifts it upwards

• It shifts it downwards

• It makes it wider

• It makes it narrower