SOLUTION: What is the transformation of the quadratic -3(x + 8)^2 - 10?

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Question 1134689: What is the transformation of the quadratic -3(x + 8)^2 - 10?
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2
quadratic function

%28x-h%29%5E2
Eight units to the right if h%3E0

%28x-h%29%5E2-k
k unit down if k%3E0

a%28x-h%29%5E2-k
stretched vertically by factor a; and if a%3C0 flipped vertically while keeping vertex (h,k).

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
What is the transformation of the quadratic -3%28x+%2B+8%29%5E2+-10?
the basic quadratic is:
f%28x%29+=+x%5E2
The standard form of a quadratic function presents the function in the form:
f%28x%29=a%28x-h%29%5E2%2Bk
so, -3%28x+%2B+8%29%5E2+-+10 we see that
you have -f%28x%29, so it reflects the function in the x-axis (that is, upside-down)
a=-3 -> if abs%28a%29%3C1, the point associated with a particular x value shifts closer to the -x - axis, so the graph appears to become wider, but in fact there is a vertical compression
h=-8->shifts eight units to the left
k=-10->the "-10" outside the function tells me that the graph is going to be moved down by ten+units

+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+x%5E2%2C-3%28x%5E2%2B16x%2B64%29-10%29+