Using the completing-the-square method, rewrite f(x) = x2 + 4x − 1 in vertex form.

1 answer:

6 0

      f(x) = x² + 4x - 1
          y = x² + 4x - 1
      y + 1 = x² + 4x - 1 + 1
      y + 1 = x² + 4x
y + 1 + 4 = x² + 4x + 4
      y + 5 = x² + 2x + 2x + 4
      y + 5 = x(x) + x(2) + 2(x) + 2(2)
      y + 5 = x(x + 2) + 2(x + 2)
      y + 5 = (x + 2)(x + 2)
      y + 5 = (x + 2)²
y + 5 - 5 = (x + 2)² - 5
      y = (x + 2)² - 5
      f(x) = (x + 2)² - 5

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14. 1.5, 10 <- Answer
15. 5,1 <- Answer

Proof 14

Solve the following system:
{2 x - y = -7 | (equation 1)
4 x - y = -4 | (equation 2)
Swap equation 1 with equation 2:
{4 x - y = -4 | (equation 1)
2 x - y = -7 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{4 x - y = -4 | (equation 1)
0 x - y/2 = -5 | (equation 2)
Multiply equation 2 by -2:
{4 x - y = -4 | (equation 1)
0 x+y = 10 | (equation 2)
Add equation 2 to equation 1:
{4 x+0 y = 6 | (equation 1)
0 x+y = 10 | (equation 2)
Divide equation 1 by 4:
{x+0 y = 3/2 | (equation 1)
0 x+y = 10 | (equation 2)
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Proof 15.

Solve the following system:
{5 x + 7 y = 32 | (equation 1)
8 x + 6 y = 46 | (equation 2)
Swap equation 1 with equation 2:
{8 x + 6 y = 46 | (equation 1)
5 x + 7 y = 32 | (equation 2)
Subtract 5/8 × (equation 1) from equation 2:{8 x + 6 y = 46 | (equation 1)
0 x+(13 y)/4 = 13/4 | (equation 2)
Divide equation 1 by 2:
{4 x + 3 y = 23 | (equation 1)
0 x+(13 y)/4 = 13/4 | (equation 2)
Multiply equation 2 by 4/13:
{4 x + 3 y = 23 | (equation 1)
0 x+y = 1 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{4 x+0 y = 20 | (equation 1)
0 x+y = 1 | (equation 2)
Divide equation 1 by 4:
{x+0 y = 5 | (equation 1)
0 x+y = 1 | (equation 2)
Collect results:
Answer: {x = 5 y = 1

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