Describe the differences between the graph of y = –3(x + 7)2 – 10 and the standard position graph of y = x2.
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please indicate whether its a 2 or a squared "(x+7)2"
yes it is squared
The parabola could be written as \(y = a(b(x-h)^2 + k\)
Where, a,b,h,k are some constants.
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a describes the vertical stretch;
b describes the horizontal stretch;
(h,k) is the vertex.
In your parabole, can you identify a,b,h and k for me? :)
y = –3(x + 7)^2 – 10
since the 3 is negative it indicate that the graph opens downward
*NOTE* if the number before the x^2 is negative the graph opens downwards, if it is positive then it opens upwards
the graph y=x^2
isnt this just y=1x^2
1 is positive so the parabola opens upwards INSTEAD of downwards.
@Brent0423 (x+7)^2 doesn't give x^2 + 49, it gives x^2 + 14x + 49.
As \((a+b)^2\ = a^2 + 2ab+b^2\)
oops thought i put that, sorry
you can still see the difference in the graphs just by looking at the number in front of the x^2
Let me find a,b,h,k for you :)
y = –3(x + 7)^2 – 10
-> y = –3(x - (-7))^2 – 10 (Notice the negative!)
-3 would be a, the vertical stretch
1 would be b, since there's nothing in front of x
Vertex would be at (-7, -10)
Now let's take a look at our basic parabola, y = x^2
a = 1
b = 1
Since our a constant is a negative number AND greater than 1, we can say that this function has been stretch vertically of factor 3.
Then b is the same.
Vertex (0,0) and (-7,-10)
We can say that the parabola is moved of 7 to the left and 10 downward.