SOLUTION: How does the graph of g(x) = (x-4)² + 3 compare to the parent function f(x) = x²? A. g(x) is shifted 4 units to the left and 3 units up. B. g(x) is shifted 3 units to the right

Question 1204759: How does the graph of g(x) = (x-4)² + 3 compare to the parent function f(x) = x²?
A. g(x) is shifted 4 units to the left and 3 units up.
B. g(x) is shifted 3 units to the right and 4 units down.
C. g(x) is shifted 4 units to the right and 3 units up.
D. g(x) is shifted 3 units to the left and 4 units up.
Found 2 solutions by math_tutor2020, josgarithmetic:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: Option C
Shift 4 units right and 3 units up

Explanation

When replacing x with x-4, we reduce the input by 4.
This will move the xy axis 4 units to the left, and gives the illusion the parabola moves 4 units to the right (when holding the parabola fixed in place compared to the moving xy axis).
I like to imagine the parabola etched in stone on a wall.
The xy axis is allowed to move left/right, which can happen through a viewfinder of a camera perhaps.

In short, x-4 means "shift 4 units right".
For students new to algebra, this may seem completely backwards.
Some new students might incorrectly think the "minus 4" means "shift left" or "shift in the negative x direction".

The +3 at the end will move the curve up 3 units because each y coordinate is 3 units larger.
A point like (5,1) moves to (5,4) as one example.

I recommend using a graphing tool like Desmos or GeoGebra to see how the transformations are taking place.
https://www.desmos.com/calculator/o42veth7sr
The order is red to blue to green
y = x^2 in red
y = (x-4)^2 in blue
y = (x-4)^2 + 3 in green

Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
x^2 made as (x-4)^2+3 is moved four units to the right and three units up.
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