Parábola that passes through (6,4) and has vertex (2,-3)

Y =  (X -2)² - 3

Step-by-step explanation:

Given as A parabola passes through (6 , 4)

And vertex of parabola = (2 , -3)

Now equation of parabola in vertex form :

Y = a (X - h)² + k       , where( h,k) are the vertex of parabola

If a is positive , the parabola open upside

If a is negative , the parabola open downside

∴ Y = a (X - 2)² + ( -3)

  As parabola passes through (6 ,4)

  4 = a (6 -2)² -3

  a =

Hence the equation of parabola with vertex is ,

   Y =  (X -2)² - 3     Answer