Question

Question #22d0b

Answer 1

`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.