QUADRATIC FUNCTIONS:

Question

QUADRATIC FUNCTIONS:

For each of the following,

a) Find the number of real roots -- find b^2-4ac: positive means 2 real roots, zero means 1 real root, negative means 0 real roots

b) Find all roots. You can use quadratic formula, completing the square, or a factoring method where applicable.

c) Find the vertex -- x = -b/2a, plug into the function to get y.

d) Plot the approximate graph -- plot the vertex exactly, then draw an upwards U shape for positive a, and downwards U shape for negative a.



1) y = x^2

2) y = x^2 - 2x + 1

3) y = -2x^2 - 3x - 4



RATIONAL FUNCTIONS:

For each of the following,

a) Factor the top and bottom and find the roots (zeros of the top) and poles (zeros of the bottom).

b) State the location of holes and vertical asymptotes -- holes happen for x-values where a root and a pole cancel out, asymptotes happen for x-values of poles which don't cancel out

c) State the location of horizontal asymptotes -- take the fraction of the highest degree terms, if the degree of the top and bottom are the same, then that will be the y-value



1) y = 1 / x

2) y = (x - 1) / (x+1)

3) y = (x^2 - x - 6) / (x^2 + 6x + 8)

Answer 1

This is homework, with clear instructions embedded.

Follow them.

 

The terminology "poles" is extremely unusual and I believe is quite non-standard.

Zeros of the denominator in a rational algebraic function give rise to a HOLE if that factor happens to exactly cancel a factor of the numerator; otherwise this is the determination of a vertical asymptote.