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Question 142831: Sketch the following function
f(x)= -x squared + 4 and
label
max or min points with appropriate coordinates
y intercept
x intercept if any
describe mathematically how the graph transformed from f(x) = x squared
Answer by Fruglemiester1234(13)   (Show Source):
You can put this solution on YOUR website! 
Max Point (0,4)
Min Point (none)
y intercept=4
x intercepts= 2, -2
X^2 automatically makes it a parabola.
When X^2 is multiplied by a negative number the parabola gets flipped over the x-axis, meaning it now opens downward.
When a +4 is added on to the equation the graph is shifted upwards four, making yur vertex, or the max point, at (0,4). This graph doesn't have a min point because the parabola goes on forever in that direction.
To do it the old fashion way all you have to do is plug n' chug. You can start by throwing in a 0 for X, which will be the Y-intercept.
-1(0)^2 + 4
0 + 4 = 4 , your points being (0,4) which you can put on your graph
Then you can throw in a 0 for Y to find the X-intercepts.
0=-1X^2+4
-4 -4 subtract 4
-4=-1X^2
/-1 /-1 divide by negative 1
4=X^2
 un-square X^2
+/-2=X, you points being (2,0)and (-2,0)
If you know what the graph should look like then you can graph knowing only these three points, but if you want more points to be sure you can plug in any number you want for either X or Y and graph them if you'f like. One thing though is you should keep the numbers simple and make sure to include negatives, especially if you're not sure what the graph should look like.
Hope that answers you question ;)
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