Find an equation in x and y whose graph contains the points on the curve C. x = 4t^2 − 5, y = 2t + 3; t in ℝ

Answer 1

Hi Hailey T.,

To find an equation in x and y for x = 4t² - 5 and y = 2t + 3, we can solve for t in one equation and plug it into the other equation.

y = 2t + 3

y - 3 = 2t

t = (y - 3)/2

x = 4t² - 5

x = 4((y - 3)/2)² - 5

x = 4((y - 3)²/2² - 5

x = (y - 3)² - 5

(x + 5) = (y - 3)², the is a parabola the opens to the right, with a vertex at (-5, 3).

I hope this helps, Joe.