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

Sure, let's rewrite the equation y = x² - 8x - 2 in the form y = a(x - h)² + k by completing the square.

Step 1: Identify a, b, and c in the equation y = ax² + bx + c In this case, a = 1, b = -8, and c = -2.

Step 2: Rewrite the equation as y = a[(x - h)² - h²] + k We can find h by using the formula h = -b/2a. Here, h = -(-8)/2*1 = 4.

Step 3: Substitute h into the equation y = 1[(x - 4)² - 4²] - 2 y = (x - 4)² - 16 - 2

Step 4: Simplify the equation 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.