Question #22d0b

1 Answer
Nov 25, 2017

#y = - (x +1)^2 +4#

Explanation:

to find the equation we start with the parabola
#y = x^2#
we have two information:

  1. reflected over the x-axis : this means it's upside down, so we add a negative sign
    #y = -x^2#

  2. vertex at (-1, 4): we can think of this from two approaches:

2.1 by using the vertex form
We can use the vertex form to answer this directly:
#y = - (x - (-1))^2 +4 #
#y = - (x +1)^2 +4#

2.2 by using the transformation # y = a*(b(x-c)^2)+d#
this means we transformed the original graph by moving up by 4 (so
#d = 4#) and to the left by -1 (so #c = -1#)
so :
#y = - (x - (-1))^2 +4 #
#y = - (x +1)^2 +4#

graph{y = -(x - (-1))^2 +4 [-10, 10, -5.21, 5.21]}

Hope this helps. Have a nice day.