Rewrite each relation in the form y = a(x − h)2 + k by completing the square. Show complete working.a. y = x2 − 8x − 2b. y = x2 − 12x + 8

a. y = x² - 8x - 2

To rewrite this equation in the form y = a(x - h)² + k, we need to complete the square.

First, group the x terms together:

y = (x² - 8x) - 2

To complete the square, we take the coefficient of x, divide it by 2, and square it. In this case, -8 divided by 2 is -4, and -4 squared is 16.

Add and subtract this inside the parenthesis:

y = (x² - 8x + 16 - 16) - 2

This simplifies to:

y = ((x - 4)² - 16) - 2

Finally, simplify the constants:

y = (x - 4)² - 18

So, the equation y = x² - 8x - 2 in the form y = a(x - h)² + k is y = (x - 4)² - 18.

b. y = x² - 12x + 8

Again, group the x terms together:

y = (x² - 12x) + 8

To complete the square, we take the coefficient of x, divide it by 2, and square it. In this case, -12 divided by 2 is -6, and -6 squared is 36.

Add and subtract this inside the parenthesis:

y = (x² - 12x + 36 - 36) + 8

This simplifies to:

y = ((x - 6)² - 36) + 8

Finally, simplify the constants:

y = (x - 6)² - 28

So, the equation y = x² - 12x + 8 in the form y = a(x - h)² + k is y = (x - 6)² - 28.