F(x)=x^2-10x+44 complete the square
1 answer:
We have that
F(x)=x²<span>-10x+44
</span><span>Group terms that contain the same variable
</span>f(x)=(x²-10x)+44
<span>Complete the square Remember to balance the equation
</span>f(x)=(x²-10x+25-25)+44
F(x)=x²<span>-10x+44
</span><span>Group terms that contain the same variable
</span>f(x)=(x²-10x)+44
<span>Complete the square Remember to balance the equation
</span>f(x)=(x²-10x+25-25)+44
Rewrite as perfect squares
f(x)=(x-5)²-25+44
f(x)=(x-5)²+19
this is the equation of a vertical parabola with vertex (5,19)
see the attached figure
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i) The given function is
The domain is
ii) For vertical asymptotes, we simplify the function to get;
The vertical asymptote occurs at
iii) The roots are the x-intercepts of the reduced fraction.
Equate the numerator of the reduced fraction to zero.
iv) To find the y-intercept, we substitute into the reduced fraction.
v) The horizontal asymptote is given by;
The horizontal asymptote is .
vi) The function has a hole at .
Thus at .
This is the factor common to both the numerator and the denominator.
vii) The function is a proper rational function.
Proper rational functions do not have oblique asymptotes.
