1 / 10

Creating Polynomials Given the Zeros.

Creating Polynomials Given the Zeros. What do we already know about polynomial functions?. They are either ODD functions. They are either EVEN functions. Linear y = 4x - 5. Cubic y = 4x 3 - 5. Quadratics y = 4x 2 - 5. Quadratics y = 4x 2 - 5. Fifth Power y = 4x 5 –x + 5.

wan
Download Presentation

Creating Polynomials Given the Zeros.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Creating Polynomials Given the Zeros.

  2. What do we already know about polynomial functions? They are either ODD functions They are either EVEN functions Linear y = 4x - 5 Cubic y = 4x3 - 5 Quadratics y = 4x2 - 5 Quadratics y = 4x2 - 5 Fifth Power y = 4x5 –x + 5 Quartics y = 4x4 - 5

  3. We know that factoring and then solving those factors set equal to zero allows us to find possible x intercepts. TOOLS WE’VE USED Long Division (works on all factors of any degree) Factoring GCF Quadratic Formula (x + )(x + ) Synthetic Division (works only with factors of degree 1) The “6” step Grouping Cubic** p/q

  4. We know that solutions of polynomial functions can be rational, irrational or imaginary. X intercepts are real. Zeros are x-intercepts if they are real Zeros are solutions that let the polynomial equal 0

  5. We have seen that imaginaries and square roots come in pairs ( + or -). So we could CREATE a polynomial if we were given the polynomial’s zeros.

  6. Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros. -1, 2, 4 Step 1: Turn the zeros into factors. (x+1)(x- 2)(x- 4) Step 2: Multiply the factors together. f(x) =x3 - 5x2 +2x + 8 x3 - 5x2 +2x + 8 Step 3: Name it!

  7. Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros. Step 1: Turn the zeros into factors. Must remember that “i”s and roots come in pairs. Step 2: Multiply factors.

  8. Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros. Step 1: Turn the zeros into factors. Must remember that “i”s and roots come in pairs. Step 2: Multiply factors.

  9. x 2 i x -2 x x x 2 -i x2 -2x x2 ix 2x x -2 x 4 x 2i 2x -2x 4 x x x x -ix -2i 1 -i2 -3 (x2- 4x + 1) (x2+ 4x + 5)

  10. x2+ 4x + 5 x2 -4x 1 4x3 x4 5x2 -20x -4x3 -16x2 4x 5 x2 f(x) = x4-10x2 -16x + 5 -3

More Related