Find two different parametric representations for the equati

Find two different parametric representations for the equation of the parabola, y = x^2 -6x + 12 (a) Let one parametric equation be x = t. Find the parametric equation for y. y = for t in (-infinity, infinity) (b) Let one parametric equation be x = t + 3. Find the parametric equation for y. y = for t in (-infinity, infinity)

Solution

y=x²-6x+12

a. When x=t we get

y= t²-6t+12

b. When x=t+3 we get

y=(t+3)²-6(t+3) +12

= t²+9 +6t -6t-18+12

= t² - 3