Polynomial functions of degree 2 or more are smooth, continuous functions. See
[link] .
To find the zeros of a polynomial function, if it can be factored, factor the function and set each factor equal to zero. See
[link],[link], and
[link] .
Another way to find the
intercepts of a polynomial function is to graph the function and identify the points at which the graph crosses the
axis. See
[link].
The multiplicity of a zero determines how the graph behaves at the
intercepts. See
[link].
The graph of a polynomial will cross the horizontal axis at a zero with odd multiplicity.
The graph of a polynomial will touch the horizontal axis at a zero with even multiplicity.
The end behavior of a polynomial function depends on the leading term.
The graph of a polynomial function changes direction at its turning points.
A polynomial function of degree
has at most
turning points. See
[link].
To graph polynomial functions, find the zeros and their multiplicities, determine the end behavior, and ensure that the final graph has at most
turning points. See
[link] and
[link].
Graphing a polynomial function helps to estimate local and global extremas. See
[link].
The Intermediate Value Theorem tells us that if
have opposite signs, then there exists at least one value
between
and
for which
See
[link].
Section exercises
Verbal
What is the difference between an
intercept and a zero of a polynomial function
The
intercept is where the graph of the function crosses the
axis, and the zero of the function is the input value for which
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits