Why does the equation (x-4)^2-28=8 have two solutions?
2 answers:
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3z-4=6z-17
-3z-4=-17 (subtracted the 6z from both sides)
-3z=-13 (added the 4 to both sides)
z=
(divided both sides by -3z)
z=
-3z-4=-17 (subtracted the 6z from both sides)
-3z=-13 (added the 4 to both sides)
z=
z=
One of the ways to graph this is to use plug in a few x-values and get an idea of the shape. Since the x values keep getting squared, there is an exponential increase on either side of the y-axis. You can see this by plugging in a few values:
When
x=0,f(x)=0
x=1,f(x)=1^2=1
x=2,f(x)=2^2=4
x=3,f(x)=3^2=9
x=4,f(x)=4^2=16
The same holds true for negative x-values to the left of the y-axis since a negative value squared is positive. For example,
x=−1,f(x)=(−1)2=1*−1=1
x=2,f(x)=(−2)2=−2*−2=4
The graph of f(x)=x^2 is called a "Parabola." It looks like this:
