math 135 ch 3

Question 1

How do you determine the amount of possible roots/zeros in a polynomial?

Answer 1

By adding the total of all degrees

Question 2

how many x-intercepts are there if the discriminant is > 0?

Answer 2

2 x-intercepts

Question 3

how many x-intercepts are there if the discriminant is equal to 0?

Answer 3

1 x-intercept

Question 4

how many x-intercepts are there if the discriminant is less that zero?

Answer 4

No x-intercepts

Question 5

How do you find the discriminant?

Answer 5

b^2-4ac

Question 6

How do you find the axis of symmetry?

Answer 6

Axis of symmetry is at the vertex, use -b/2a and f(-b/2a)

Question 7

How do you know if an x-value is a lower bound?

Answer 7

The results of synthetic division show an alternation of positive and negative values.

Question 8

How do you know if an x-value is an upper bound?

Answer 8

The results of synergies division show all positive values.

Question 9

How do we know if an x-value is a zero/root to a polynomial?

Answer 9

• check by synthetic division where c=0
• r=c therefore the x-value is a factor of the polynomial

Question 10

How to tell the number of possible positive real zeros in a polynomial?

Answer 10

The potential amount of positive real zeros in a polynomial is equal to or less than by an even number of the number of sign variations in the polynomial.

Question 11

How to tell the potential number of negative real zeros of a polynomial.

Answer 11

The number is equal to or less than by an even number of the amount of sign changes in f(-x).

Question 12

How to tell the number of potential negative real zeros of a polynomial?

Answer 12

The number is equal to or less than by an even number of the amount of sign changes in f(-x).

Question 13

What is the conjugate zero theorem?

Answer 13

If a real zero of a polynomial is a conjugate, then so is its complex conjugate.

Question 14

Explain the patterns of graph behaviors of polynomials

Answer 14

• x-values with a negative highest degree show that the ends are left down right up unless the coefficient is of negative value.
• values with a positive highest degree form a parabola and open down of the coefficient is of negative value.
• if the multiplicity is odd, the the graph cross the x-axis at the x-intercept.
• if the multiplicity is even, the the graph just touches the x-axis at the x-intercept.

Question 16

How do you find limitations of a polynomial?

Answer 16

Look to highest degree of the polynomial for limitations in positive and negative infinity
Look to the constant for limitations towards zero, the limit is = to the constant.

Question 17

How do you find the lead term of a factored polynomial?

Answer 17

Add all multiplicities, the sum is the lead term

Question 18

What do the zeros of polynomials tell us?

Answer 18

A zero either reveals a vertical asymptote or a hole

Question 19

What is the horizontal asymptote if the highest degree of the numerator is more than the degree of the denominator?

Answer 19

There is no HA

Question 20

What is the horizontal asymptote if the highest degree of the numerator is less than the degree of the denominator?

Answer 20

y=0

Question 21

What is the HA if the highest degree in the numerator and denominator are equal?

Answer 21

Divide thea coefficients of the num and denom to get HA

Question 22

How do you find slant asymptote?

Answer 22

Oblique exists if the degree of the numerator is only higher than the degree of the denominator by 1. Do long division, ignore the remainder. The quotient is the location of the slant asymptote.

Question 23

How do you format the vertical asymptotes?

Answer 23

As individual x-values and not in sets.