arenceabigns

2020-11-01

For the following exercise, for each polynomial $f\left(x\right)=\text{}\frac{1}{2}{x}^{2}\text{}-\text{}1$ :
a) find the degree,
b) find the zeros, if any,
c) find the y-intercept(s), if any,
d) use the leading coefficient to determine the graph’s end behavior,
e) determine algebraically whether the polynomial is even, odd, or neither.

Luvottoq

Skilled2020-11-02Added 95 answers

a) Since degree of polynomial is the greatest power of x, then the degree of $f\left(x\right)=\text{}\frac{1}{2}{x}^{2}\text{}-\text{}1\text{}is\text{}2$
b) To find the zeros:
$f\left(x\right)=0$

$\frac{1}{2}{x}^{2}\text{}-\text{}1=0$

${x}^{2}\text{}-\text{}2=0$
Then:
$x=\text{}\pm \text{}\sqrt{2}$
c) To find y-intercept, put $x=0$ , then y-intercept is -1.
d) Here $n=2,\text{}\text{even and}\text{}{a}_{n}=\text{}\frac{1}{2}\text{}\text{}0$ , then graph rises to the left and right.
e) To determine whether the polinomial is even, odd, or neither, replace z with -x:
$f(-x)=\text{}\frac{1}{2}{(-x)}^{2}\text{}-\text{}1$

$=f\left(x\right)$
Then function is even.

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