Completing the Square Worksheet

Completing the Square

Read each question carefully and follow the instructions to complete the square. Show all your work for full credit.

1. To complete the square for x² + bx, you add ( )² to the expression.

2. Completing the square transforms a quadratic expression into the form (x +  )² + k.

3. Rewrite the quadratic function f(x) = x² + 6x + 5 in vertex form by completing the square.

4. Rewrite the quadratic function g(x) = x² - 10x + 21 in vertex form by completing the square.

5. Completing the square can only be used to solve quadratic equations with a leading coefficient of 1.

6. The process of completing the square always results in real solutions for quadratic equations.

7. What constant term must be added to x² + 12x to complete the square?

8. Which of the following is equivalent to x² - 8x + 16?

9. Solve the equation x² + 4x - 12 = 0 by completing the square.

10. Solve the equation 2x² - 8x + 6 = 0 by completing the square.

11. The height h (in feet) of a projectile launched vertically upward from the ground with an initial velocity of 64 ft/s is given by h(t) = -16t² + 64t. Use completing the square to find the maximum height of the projectile and the time it takes to reach that height.