Maximum and Minimum Values of General Quadratic Functions
1 answer:
Answer:
x=-1
y=15
Step-by-step explanation:
This works because completing the square is essentially demonstrating what g(x) - where g(x) in this case = x^2 - would have to be translated by to give the function you have.
So by completing the square you have shown that the function you've been given has been shifted to the left by -1, stretched by a factor of 2 along the y axis and shifted up by 15.
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Answer:
- zeros: x = -3, -1, +2.
- end behavior: as x approaches -∞, f(x) approaches -∞.
Step-by-step explanation:
I like to use a graphing calculator for finding the zeros of higher order polynomials. The attachment shows them to be at x = -3, -1, +2.
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The zeros can also be found by trial and error, trying the choices offered by the rational root theorem: ±1, ±2, ±3, ±6. It is easiest to try ±1. Doing so shows that -1 is a root, and the residual quadratic is ...
x² +x -6
which factors as (x -2)(x +3), so telling you the remaining roots are -3 and +2.
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For any odd-degree polynomial with a positive leading coefficient, the sign of the function will match the sign of x when the magnitude of x gets large. Thus as x approaches negative infinity, so does f(x).
