SOLUTION: 1. The graph of y=-1/2x^2 shifted 3 units to the right and 3 units upward. 2. the graph of y=-4x^2 shifted 8 units to the left and 4 units downward. 3. the graph of y=3/4x^2 shif

Question 1192297: 1. The graph of y=-1/2x^2 shifted 3 units to the right and 3 units upward.
2. the graph of y=-4x^2 shifted 8 units to the left and 4 units downward.
3. the graph of y=3/4x^2 shifted 2 units to the left and 2 units downward.
THanks..
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
The standard form of a quadratic function presents the function in the form

the basic parabola graph of f(x)=x^2 is horizontally shifted left (h < 0) and right (h > 0)
vertically shifted up (k > 0) or shift it down (k < 0) .
1. The graph of shifted units to the right and units upward.
if shifted units to the right =>
if shifted units upward=>

2. the graph of shifted units to the left and units downward.
units to the left =>
units downward=>

3. the graph of units to the left and units downward.
units to the left =>
units downward=>

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
y = -1/2 * x^2 becomes y = -1/2 * (x-3)^2 + 3
here's the graph.

y = -4 * x^2 becomes y = -4 * (x+8)^2 - 4
here's the graph.

y = 3/4 * x^2 becomes y = 3/4 * (x+2)^2 - 2
here's the graph.

i believe these are called transformations.

here's a reference on transformations.
https://www.mathsisfun.com/sets/function-transformations.html

here's another one.
https://www.purplemath.com/modules/fcntrans.htm

just go to the internet and do a search on algebra transformations and a whole bunch will pop up.

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