Question

3. Fill in the blanks with the correct numbers following the appropriate steps to complete the square of the following quadratic

equation.
Step 1: Move the constant to the right side of the equation.
Step 2: Simplify both sides of the equation.
Step 3: Complete the square by adding half the middle term squared to both sides of the equation.
Step 4: Factor the left side of the equation since it is a perfect square trinomial and simplify the right side.
Step 5: Move the constant back to the left side of the equation, this will leave the equation in vertex form.
x² + 4x-11 = y
Step 1: x² + 4x - 11+
Step 2: x² + 4x =
Step 3: x² + 4x+
Step 4: (x+
Step 5: (x+
Points
)² =
0²-
HE
=0+
0
27

Answer 1

To complete the square for the equation x² + 4x - 11 = y, the constant is moved to the right side, 4 is added to both sides after dividing the middle coefficient by 2 and squaring it, the equation is factored into a perfect square, and the constant is moved back to get the equation in vertex form.

Step-by-step explanation:

To complete the square of the quadratic equation x² + 4x - 11 = y, follow these steps:

1. Move the constant term to the right side of the equation: x² + 4x = y + 11.
2. There is no simplification needed since the coefficient of x² is 1 and there are no like terms to combine.
3. Add (4/2)² = 4 to both sides to complete the square: x² + 4x + 4 = y + 11 + 4.
4. Now, factor the left side which is a perfect square trinomial: (x + 2)² = y + 15.
5. Finally, move the constant back to the left side of the equation to put it in vertex form: (x + 2)² - 15 = y.