Answer:
[tex]y=x^2+5x+20\\ \\ y=8x^2+35[/tex]
Explanation:
The end behavior of a rational function is the limit of the function as x approaches negative infinity and infinity.
Note that the the values of even functions are the same for ± x. That implies that their limits for ± ∞ are equal.
The limits of the quadratic function of general form [tex]y=ax^2+bx+c[/tex] as x approaches negative infinity or infinity, when [tex]a[/tex] is positive, are infinity.
That is because as the absolute value of x gets bigger y becomes bigger too.
In mathematical symbols, that is:
[tex]\lim_{x \to -\infty}3x^2=\infty\\ \\ \lim_{x \to \infty}3x^2=\infty[/tex]
Hence, the graphs of any quadratic function with positive coefficient of the quadratic term will have the same end behavior as the graph of y = 3x².
Two examples are:
[tex]y=x^2+5x+20\\ \\ y=8x^2+35[/tex]
