If the parabola represented by y=-(x-2)^2 + 5 is translated 3 units

Fdambro294
"Finally, to reflect the parabola into the X Axis, we must Negate the Sign of the Entire Input of the Function
"

Please explain this.
What does "reflect the parabola across X axis" mean?

Greetings,

The way I understood the “shifting” of the quadratic function was as follows.

If you start with the simple quadratic function:

y = (x)^2

Graph a few points just to see the general idea.

Now, if you negate the entire input (meaning negate the entire right side of the equation)

y = - (x)^2

the output (the y value) will appear on the negative side of the X -Axis line.

Before: (2 , 4) and (-2 , 4) were on —-> y = (x)^2

Now: (2 , -4) and (-2 , -4) will be on —-> y = - (x)^2

It will be like we took the entire graph of y = (x)^2 and flipped it over the X-axis

We are going to do the same thing with the given function. Negate everything on the right side so that whatever the Y value was before, the new Y value will appear in the “mirror image” on the opposite side of the X-Axis.

After shifting the function 3 spots to the left we have:

y = - (x + 1)^2 + 5

Every point that shows up on this graph will be 3 points to the left of the corresponding point in the original.

Now negating the right side:

y = (-1) * [- (x + 1)^2 + 5 ]

y = (x + 1)^2 - 5

I guess “entire input” wasn’t the best phrase to use. I believe that was a late night lol

Does that help, I hope?





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