2526PythHigherDegree

Question 1

What must a triangle have to use the Pythagorean formula?

Answer 1

a right angle

Question 2

What is the longest leg of a right triangle called?

Answer 2

Hypotenuse

Question 3

What are the other 2 sides called?

Answer 3

Legs

Question 4

What is the Pythagorean Theorem?

Answer 4

The squares of the lengths of the 2 legs of a right triangle = the square of the hypotenuse.

a² + b² = c²

Question 5

If one of the legs is 10 units long and the hypotenuse is 26 units long, how long is the other leg?

Answer 5

10² + b² = 26²

100 + b² = 676

b² = 576

b = 24

Question 6

Is there a right triangle where the legs are only 1 unit apart and the hypotenuse is 29?

Answer 6

a² + (a + 1)² = 29²

a² + a² + 2a + 1 = 841

2a² + 2a - 840 = 0

a² + a - 420 = 0

(a + 21)(a - 20) = 0

21,20

Question 7

What are Pythagorean Triples?

Answer 7

A series of 3 numbers where the first number squared + the second number squared = the third number squared

Question 8

What is the smallest Pythagorean Triple?

Answer 8

3,4,5

Question 9

What are scaled-up Pythagorean Triples?

Answer 9

If 3,4,5 is a triple, then so is 6,8,10 and

9,12,25 and

30,40,50, etc.

Question 10

How many Pythagorean Triples are there?

Answer 10

An infinite number.

There are also an infinite number of Triples of just the scaled-up triples of, say 3,4,5

Question 11

What do most lists of Pythagorean Triples not include?

Answer 11

The scaled-up ones.

Question 12

What is a Primitive Triple?

Answer 12

It is a Triple that is not scaled up.

In Primitive Triples, a,b, and c have no common factors.

^{(A common factor would be the scale)}

Question 13

How do odd and even numbers fit with Pythagorean Triples?

Answer 13

Pythagorean Triples are either:

(1) All even (scaled by 2)

or

(2) 2 odd numbers and 1 even number

Question 14

What are required of polynomials of higher order?

Answer 14

The exponents must be integers.

Question 15

How is the degree of a polynomial named?

Answer 15

By the largest exponent.

14x³ + 2x² + x - 4

is a third-degree polynomial.

Question 16

What is the leading coefficient of a polynomial equation?

Answer 16

The coefficient of the highest exponent:

4x³ + 3x² + 2x - 1

Question 17

What is true of the graph of a polynomial equation?

Answer 17

It is continuous and has no sharp corners

Question 18

What is the largest number of x-intercepts in any polynomial equation?

Answer 18

The largest degree of the polynomial.

Question 19

What do the ends of the graphs of polynomial equations never do?

Answer 19

Flatten out.

Question 20

What does the polynomial tell you about the direction of the endpoints?

Answer 20

If the highest degree is even, both go up or both go down.

If the degree is odd, one goes up and the other goes down.

^{If the leading coefficient is positive the left goes down and the right goes up.}

Question 21

Which components of a polynomial have the greatest influence on its graph?

Answer 21

The highest degree polynomial and

the leading coefficient.