SOLUTION: whats the equation of the parabo0la vertext at (-4,5) passes thru (0,9)

Two ways:

1. If you've had this equation for a parabola

(x - h)² = 4p(y - k)

2. If you've had this equation for a parabola

y = a(x - h)² + k

I'll do it both ways.  Either way (h,k) = (-4,5), (x,y) = (0,9)

1. If you've had this equation for a parabola

   (x - h)² = 4p(y - k)
(0 - (-4))² = 4p(9 - 5)
  (0 + 4)²  = 4p(4)
         4² = 16p
         16 = 16p
          1 = p
Rewrite original:

   (x - h)² = 4p(y - k)
(x - (-4))² = 4(1)(y - 5)
   (x + 4)² = 4(y - 5)

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2. If you've had this equation for a parabola

   y = a(x - h)² + k
   9 = a(0 - (-4))² + 5
   9 = a(0 + 4)² + 5
   9 = a(4)² + 5
   9 = a(16) + 5
   9 = 16a + 5
   4 = 16a
4/16 = a
 1/4 = a

Rewrite original equation

   y = (1/4)(x - (-4))² + 5
   y = (1/4)(x + 4)² + 5

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Either way the graph is



Edwin