Graphs

Graphs

Site: | TBAISD Moodle |

Course: | Michigan Algebra I Preview 2012 |

Book: | Graphs |

Printed by: | Guest user |

Date: | Saturday, July 20, 2019, 02:41 PM |

From A Graph

The steps to model a polynomial function from a graph are very similar to the steps used when given a table. First, determine the zeros of the function by looking at the graph. Second, turn each zero into a factor of the function. Finally, determine the factored form of the polynomial.**Example 1** Determine the function that models the graph below:

*Step 1.* Determine the zeros of the function.

(-1, 0), (0, 0), (5, 0)

*Step 2.* Turn each zero into a factor of the function.

Since *x* = -1, then (*x* + 1) is a factor of the polynomial.

Since *x* = 0, then (*x*) is a factor of the polynomial.

Since *x* = 5, then ( *x* - 5) is a factor of the polynomial.

Example 1 Continued

*y* = *a* (*x* + 1)(*x*)(*x* - 5); point (4, -40)

-40 = *a* (4 + 1)(4)(4 - 5)

-40 = *a* (5)(4)(-1)

-40 = *a* (-20)

2 = *a*

Example 2

Determine the function that models the graph below:

*Step 1.* Determine the zeros of the function.

(-5, 0), (0, 0), (2, 0), (3, 0)

*Step 2.* Turn each zero into a factor of the function.

Since *x* = -5, then (*x* + 5) is a factor of the polynomial.

Since *x* = 0, then (*x*) is a factor of the polynomial.

Since *x* = 2, then (*x* - 2) is a factor of the polynomial.

Since *x* = 3, then (*x* - 3) is a factor of the polynomial.

*Step 3.* Determine the factored form of the polynomial by using another point from the graph. Substitute the point in for (*x, y*) and solve for the value of *a*.

*y* = *a* (*x* + 5)(*x*)(*x* - 2)(*x* - 3); point (-2, -60)

-60 = *a* (-2 + 5)(-2)(-2 - 2)(-2 - 3)

-60 = *a* (3)(-2)(-4)(-5)

-60 = *a* (-120)

.5 = *a*