How do you solve #y=-2(x+5)^2-2#?

1 Answer
Alan P.
Jun 27, 2015

#y=-2(x+5)^2-2# is a continuous function with an infinite number of #(x,y)# pairs which could be considered solutions.
There is no "solution".

Explanation:

graph{-2(x+5)^2-2 [-14, 6, -9.08, 0.92]}

We could find the solutions for a couple of points that are often of interest.

The equation itself is in the "vertex form" and we can read the coordinates of the vertex directly from the equation: #(-5,-2)#

The line represented by this equation does not touch the x-axis,
so there is no x-intercept.

However, we can determine the coordinates of the y-intercept by setting #x=0# in the equation and solving for #y#
#y = -2(0+5)^2-2 = -52#
So the y-intercept occurs at #(0,-52)#

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