Create the quadratic function that contains the points (0-2), (1, 0) and (3, 10). Show all of your work for full credit.
1 answer:
Answer:
My graphing calculator tells me the function is
.. f(x) = x^2 +x -2
_____
Since we recognize the y-intercept as being (0, -2), we only need to find the coefficients of x and x^2.
If you want to do this by hand, you can use
.. y = ax^2 +bx -2
to write 2 equations in a and b for the (x, y) values (1, 0) and (3, 10).
.. 0 = a +b -2
.. 10 = 9a +3b -2
To solve by substitution, you can let a = 2-b, and you have
.. 10 = 9(2 -b) +3b -2
.. 6b = 6 . . . . . . . . . . . add 6b-10
.. b = 1
.. a = 2 -1 = 1
Step-by-step explanation:
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Assuming I understand your question correctly, in that you’re looking for just some descriptions of the differences between the functions. If so, then I’d say:
First graph both functions, the f(x) and the g(x). Then spot the differences.
Note that the g(x) function has shifted towards the right compared with the f(x) function.
Another way that the g(x) differs from the f(x) function is that it’s stretched. The vertex is in the IV quadrant for g(x) rather than at the origin for f(x).
I hope that helps.
First graph both functions, the f(x) and the g(x). Then spot the differences.
Note that the g(x) function has shifted towards the right compared with the f(x) function.
Another way that the g(x) differs from the f(x) function is that it’s stretched. The vertex is in the IV quadrant for g(x) rather than at the origin for f(x).
I hope that helps.