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

Algebra ->  Linear-equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
The standard form of a quadratic function presents the function in the form
f%28x%29=a%28x-h%29%5E2%2Bk
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 y=-%281%2F2%29x%5E2 shifted 3 units to the right and 3 units upward.
if shifted 3 units to the right =>h=3
if shifted 3 units upward=>k=3
y=-%281%2F2%29%28x-3%29%5E2%2B3



2. the graph of y=-4x%5E2 shifted 8+units to the left and 4+units downward.
8 units to the left =>h=-8
4 units downward=>k=-4
y=-4%28x-%28-8%29%29%5E2-4
y=-4%28x%2B8%29%5E2-4

+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+-4x%5E2%2C+-4%28x%2B8%29%5E2-4%29+

3. the graph of y=%283%2F4%29x%5E2+shifted+%7B%7B%7B2+units to the left and 2 units downward.
2 units to the left =>h=-2
2 units downward=>k=-2
y=%283%2F4%29%28x%2B2%29%5E2-2




Answer by Theo(13342) About Me  (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.