Vocab and Concepts - Quadratic Functions and Equations

Question 1

What is the definition of i?

Answer 1

√-1

Question 2

What is determined in a function when y=0?

Answer 2

x- intercepts

Question 3

What is determined in a function when x=0?

Answer 3

y-intercepts

Question 4

What is standard form of a quadratic function?

Answer 4

y= ax² + bx + c

Question 5

What is vertex form of a quadratic function

Answer 5

y= a(x-h)² + k

Question 6

What must one use first when given the standard form of the quadratic function?

Answer 6

x= -b/2a

Question 7

What is the difference between instructions to factor or factor completely and instructions to solve?

Answer 7

A factoring problem does not have an equal sign.

Question 8

When a graph is translated to the left, the number of spaces should be ______ from x.

Answer 8

Subtracted

Question 9

When a graph is translated to the right, the number of spaces should be ______ from x.

Answer 9

Added

Question 10

What method of factoring should always be attempted first?

Answer 10

Common monomial

Question 11

What method is used if an expression will not factor?

Answer 11

Quadratic formula

Question 12

What is the quadratic formula?

Answer 12

x= -b±√b²-4ac/2a

Question 13

The “k” or y-coordinate of the vertex is always equal to the ______ or ______ of a function.

Answer 13

Maximum or minimum

Question 14

How can we obtain a quadratic regression given a table of values?

Answer 14

Stat→ edit→L₁ , L₂ → stat→calc→5→ enter

Question 15

To find a minimum or maximum, one must simply find the _____.

Answer 15

Vertex

Question 16

Explain how to rationalize a complex number.

Answer 16

Take the conjugate of the denominator and use FOIL (sometimes distributive) to multiply it by both the numerator and denominator.

Question 17

What are the four things we find when we set a quadratic equal to zero and solve?

Answer 17

1. Zeros
2. Solutions
3. X-intercepts
4. Roots

Question 18

When we are given a vertex (h,k) and a point (x,y) to find an equation of a parabola, what is the value we have left to find?

Answer 18

a

Question 19

What is the discriminant and what does it tell us?

Answer 19

b²-4ac - It tells us the number and kind of solutions.
b²-4ac > 0, 2 real
b²-4ac = 0, 1 real
b²-4ac < 0, 2 imaginary

Question 20

Show an example of a factor pair and factor it.

Answer 20

a² - 5a -14= (a-5) (a+7)

Question 21

Show an example of a difference of squares and factor it.

Answer 21

16x² - 2y²
(4x)² - (5y)²
(4x-5y) (4x+5y)

Question 22

Show an example of trial and error and factor it.

Answer 22

2x² +11x +12
2x² +8x+3x+12
(2x²+8x) (3x+12)
2x(x+4) +3(x+4)
(x+4) (2x+3)