Solving Quadratic Equations: Completing the Square (Continued) Assignment

Complete the steps for solving 7 = -2x^2 + 10x.

-2 Add 25/4 subtract 25/2 5/2

Which are steps that could be used to solve 0 = 9(x2 + 6x) - 18 by completing the square? Check all that apply.

1st and 4th

Which are steps in the process of completing the square used to solve the equation 3 - 4x = 5x2 - 14x? Check all that apply.

2nd 4th 7th

Solve the quadratic function by completing the square. What are the missing pieces in the steps?

50 3 -8

Complete the steps in solving the quadratic function 7x - 9 = 7x2 - 49x by completing the square.

56 112 16

Determine the missing step for solving the quadratic equation by completing the square.

Add 4 subtract 24 from 5 2

What are the zeros of the quadratic function f(x) = 6x2 - 24x + 1?

D

Andy is solving a quadratic equation using completing the square. If a step in the process results in = (x - 6)2, could the original quadratic equation be solved by factoring? Explain your reasoning.

Yes, the equation can be solved by factoring. Using the given equation, take the square root of both sides. Both 169 and 9 are perfect squares, so the left side becomes plus or minus 13/3, which is rational. Six plus 13/3 is a rational number, and 6 minus 13/3 is also a rational number. If the solutions of a quadratic equation are rational, then the equation is factorable.

Penelope determined the solutions of the quadratic function by completing the square. f(x) = 4x2 + 8x + 1 -1 = 4x2 + 8x -1 = 4(x2 + 2x) -1 + 1 = 4(x2 + 2x + 1) 0 = 4(x + 2)2 0 = (x + 2)2 0 = x + 2 -2 = x What error did Penelope make in her work?

(C) Penelope should have added 4 to both sides instead of adding 1.