Question

3. Complete the square for the following equations:

Answer 1

The square for the  equation:  $y=2x^{2} + 12x +1$ is $y=2(x+3)x^{2} -17$

The square for the  equation:  $y=4x^{2} +48x-10$ is $y=4(x+6)x^{2} -154$

a)

$y=2x^{2} +12x +1$

$y = 2[(x^{2} + 6x)] + 1$ ( taking common)

$y = 2[(x+3)^{2} - 9] + 1$ ( adding and subtracting 9 to make a square term

$y = 2(x+3)^{2} - 18 + 1$ ( multiplying by 2)

$y=2(x+3)x^{2} -17$

b)

$y=4x^{2} +48x-10$

$y = 4[(x^{2} + 12x)] - 10$  (taking 4 common)

$y = 4[(x+6)^{2} - 36)] - 10$ (adding and subtracting 36)

$y = 4(x+6)^{2} - 144 - 10$(multiplying by 4)

$y=4(x+6)x^{2} -154$

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