[Problem Solving 2] *
2 answers:
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Answer:
Step-by-step explanation:
I used logic and took the easy way around this as opposed to the long, drawn-out algebraic way. I noticed right off that at x = -3 and x = -1 the y values were the same. In the middle of those two x-values is -2, which is the vertex of the parabola with coordinates (-2, 4). That's the h and k in the formula I'm going to use. Then I picked a point from the table to use as my x and y in the formula I'm going to use. I chose (0, 3) because it's easy. The formula for a quadratic is
and I have everything I need to solve for a. Filling in my h, k, x, and y:
and
and
-1 = 4a so
In work/vertex form the equation for the quadratic is
In standard form it's:
Note that the graph of the function 
has 2 asymptotes:
The horizontal asymptote x=0,
and the vertical asymptote y=0, as shown in the first picture.
Adding 2/9 to this function, creating
, shifts the first graph 2/9 units up. It also shifts the horizontal asymptote y=0 to t=2/9.
We can express the function as
.
Answer:
The horizontal asymptote x=0,
and the vertical asymptote y=0, as shown in the first picture.
Adding 2/9 to this function, creating
We can express the function as
Answer: