# 2.2 Polynomial Functions - HP Pre-calc

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Leading coefficent:

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## Tags and Description

### 23 Terms

1

Leading coefficent:

the coefficent of the variable with the highest exponent

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2

Degree of a Function:

Highest exponent of any of the terms in the polynomial

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3

Whats the name of a function with a degree of 0?

Constant

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4

Whats the name of a function with a degree of 1?

Linear

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5

Whats the name of a function with a degree of 2?

Quadratic

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6

Whats the name of a function with a degree of 3?

Cubic

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7

Whats the name of a function with a degree of 4?

Quartic

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8

Whats the name of a function with a degree of 5?

Quintic

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9

Whats the name of a function with a degree of 6, and so on?

Degree of 6, degree of (degree of function)

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10

What would a function NOT look like?

Anything with sharp turns or piecewise functions

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11

Even degree and a positive leading coefficient means:

Arrows pointing up in the same direction (U shape)

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12

Even degree and a negative leading coefficient means:

Arrows pointing down in the same way (n shape)

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13

Odd degree and a positive leading coefficient means:

Arrows pointing in opposite directions, with the right arrow pointing up and the left pointing down

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14

Odd degree and a negative leading coefficient means:

Arrows pointing in opposite directions, with the right arrow pointing down and the left pointing up

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15

Turning point:

When the graph changes from increasing to decreasing, or vice versa

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16

If you have a polynomial of degree n, how many turning points do you have?

n-1

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17

How many x-intercepts will you have if given a polynomial of a degree of n?

N solutions, and it can have UP TO n roots

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18

Whats the difference between roots and solutions?

While solutions are all answers for the x-intercept (counting multiplicities and imaginary numbers), not all can be represented on a graph as roots (like imaginary numbers, as they dont touch the x-axis, so they can't be counted as x-intercepts)

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19

Multiplicity:

Number of times a solution appears

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20

When a multiplicity is 1 (ex: (x+1)):

Graph crosses the x-axis at that root one time

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21

When a multiplicity is even (ex: (x+1)^2):

Graph is tangent the x-axis at that root (it touches the line, doesn't cross it, and goes back the direction it came)

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22

When a multiplicity is odd (ex: (x+1)^3):

Graph crosses through the x-axis with a point of inflection at that root

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23

Can a root of imaginary numbers of a polynomial function cross the x-axis?

It can NEVER cross the x-axis, therefore we dont label imaginary roots on graphs

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