name:__________ warm-up 5-4 state the degree and leading coefficient of –4x 5 + 2x 3 + 6. find...

Name:__________ warm-up 5-4

State the degree and leading coefficient of

–4x5 + 2x3 + 6.

Find p(3) and p(–5) for p(x) = x3 – 10x + 40.

Determine whether the statement is sometimes, always, or never true.The graph of a polynomial of degree three will intersect the x-axis three times.

Describe the end behavior of the graph of functionf(x) = –x2 + 4

Details of the DayEQ:How do polynomials functions model real world problems and their solutions?

I will be able to…•Graph polynomial functions and locate their zeros.

•Find the relative maxima and minima of polynomial functions.

Activities:Warm-upReview homeworkNotes: Class work/ HW

MP Exam – Thursday, November 13 All make-up work due Monday, November 1 no exceptions

Vocabulary:•Location Principle•relative maximum•relative minimum•extrema•turning points

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A Quick Review State the degree and leading coefficient of

–4x5 + 2x3 + 6.

Find p(3) and p(–5) for p(x) = x3 – 10x + 40.

Determine whether the statement is sometimes, always, or never true.The graph of a polynomial of degree three will intersect the x-axis three times.

Describe the end behavior of the graph of functionf(x) = –x2 + 4

Notes and examplesState the degree and leading coefficient of 7z3 – 4z2 + z. If it is not a polynomial in one variable, explain why.

State the degree and leading coefficient of 6a3 – 4a2 + ab2. If it is not a polynomial in one variable, explain why

State the degree and leading coefficient of 3x5 + 2x2 – 4 – 8x6. If it is not a polynomial in one variable, explain why

. Determine whether 3x3 + 2x2 – 3 is a polynomial in one variable. If so, state the degree and leading coefficient.

Notes and examplesGraph f(x) = –x3 – 4x2 + 5 by making a table of values.

Graph f(x) = –x3 – 4x2 + 5 by making a table of values.

Which graph is the graph of f(x) = x3 + 2x2 + 1?

Notes and examples

Notes and examplesDetermine consecutive values of x between whicheach real zero of the function f(x) = x4 – x3 – 4x2 + 1 is located. Then draw the graph.

Notes and examples

Look at the values of f(x) to locate the zeros. Then use the points to sketch the graph of the function.

There are zeros between x = –2 and –1, x = –1 and 0, x = 0 and 1, and x = 2 and 3.

Notes and examplesGraph f(x) = x3 – 3x2 + 5. Estimate the x-coordinates at which the relative maxima and relative minima occur.

Notes and examplesYou can use a graphing calculator to find the

relative maximum and relative minimum of afunction and confirm your estimate.Enter y = x3 – 3x2 + 5 in the Y= list and graphthe function.Use the CALC menu to find each maximumand minimum.When selecting the left bound, move thecursor to the left of the maximum orminimum. When selecting the right bound,move the cursor to the right of the maximumor minimum.

The estimates for a relative maximum near

x = 0 and a relative minimum near x = 2 are

accurate.

Notes and examplesConsider the graph of f(x) = x3 + 3x2 + 2. Estimate the x-coordinates at which the relative maximum and relative minimum occur.A. relative minimum: x = 0relative maximum: x = –2

B. relative minimum: x = –2relative maximum: x = 0

C. relative minimum: x = –3 relative maximum: x = 1

D. relative minimum: x = 0relative maximum: x = 2

Notes and examplesA. HEALTH The weight w, in pounds, of a patient during a 7-week illness is modeled by the function w(n) = 0.1n3 – 0.6n2 + 110, where n is the number of weeks since the patient became ill.Graph the equation.

Notes and examples

Notes and examplesDescribe the turning points of the graph and its end behavior.

Notes and examplesWhat trends in the patient’s weight does the graph suggest?

Is it reasonable to assume the trend will continue indefinitely?

Notes and examples. WEATHER The rainfall r, in inches per month, in a Midwestern town during a 7-month period is modeledby the function r(m) = 0.01m3 – 0.18m2 + 0.67m + 3.23, where m is the number of months after March 1.Graph the equation.

Describe the turning points of the graph and its end behavior

WEATHER What trends in the amount of rainfall received by the town does the graph suggest?

Is it reasonable to assume the trend will continue indefinitely?