GRAPHING POLYNOMIAL FUNCTIONS! (YOU SHOULD PROBABLY WRITE THIS DOWN)

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Presentation transcript:

GRAPHING POLYNOMIAL FUNCTIONS! (YOU SHOULD PROBABLY WRITE THIS DOWN)

The steps 1.Find the end behavior. 2.Find the y-intercept 3.Find the x-intercepts (account for all, multiplicity) a. If function is a quadratic then factor or use formula b. If a factor is given,use division to find remaining intercepts. 4.Plot all points found above and complete graph.

Lets start with this one: If leading X is Positive Odd degree Even degree If leading X is negative Odd degree Even degree

The x-intercepts: We find these by setting all of our factors equal to 0 and solving for x. So our x-intercepts are: (1,0) (3,0) and (-2,0)

Let’s Pause to see what out Graph looks like now: First we put in our x-intercepts Which were: (-2,0) (1,0) and (3,0 ) Next we put in our y-intercept Which was: (0,6)

Multiplicity

Multiplicity cont.

From there we just have to connect with a curve.

Reminder of the steps: 1.Find the end behavior. 2.Find the y-intercept 3.Find the x-intercepts (account for all, multiplicity) a. If function is a quadratic then factor or use formula b. If a factor is given, use division to find remaining intercepts. 4.Plot all points found above and complete graph.

Try this one

Plot the x-intercepts. Plot the y-intercept Plot the end behavior Plot Multiplicity Sketch graph

New topic: Synthetic division

Synthetic Division Example Multiply Add

0 remainder, so f (2) = 0 and (x – 2) is a factor. Take the result of this division and perform synthetic division again using the factor (x + 3). 0 remainder, so f (–3) = 0 and (x + 3) is a factor.

Because the remainder is r = –9, you can conclude that x = -2 is not a factor of the polynomial. If this happens we have to follow other steps to find the solutions, that we will learn later.

Next topic: Finding, creating, polynomials Find the polynomial with the given roots: 2, -3 and 1 If there are 3 roots the final answer will be a cubic function. Write the given solutions as factors: (x – 2) (x - -3) ( x – 1) and the second will become (x +3) Now multiply all the factors together to find the polynomial (x – 2)(x + 3) ( x – 1) Final Answer

Find the polynomial with the given roots. A root at -4, 0, and a double root at 2.

Now we just have to practice more!