Chpt. 4, Quadratics

Question 1

parabola

Answer 1

The graph of a quadratic function. It is the set of all points P in a plane that are the same distance from a fixed point F, as they are from a line d, the directrix.

Question 2

quadratic function

Answer 2

A function that has a variable raised to the second degree. It can be written in the form f(x) = ax^2 +bx +c, where a does not equal zero.

Question 3

vertex form of a quadratic function

Answer 3

F(x) = (x -h)^2 +k, where a does not equal zero, and where (h, k) are the coordinates for the vertex of the function.

Question 4

axis of symmetry

Answer 4

The line that divides a figure into two parts that are mirror images of each other.

Question 5

vertex of a parabola

Answer 5

The point where the function of the parabola reaches a maximum or minimum value. The parabola intersects it’s axis of symmetry at the vertex.

Question 6

minimum value

Answer 6

The minimum value of a function y = f(x) is the least y-value of the function. It is the y-coordinate of the lowest value on the graph of f.

Question 7

maximum value

Answer 7

The maximum value of a function y = f(x) is the greatest y-value of the function. It is the y-coordinate of the highest point on the graph of f.

Question 8

exponential function transformations, from parent:

f(x) = x^2

to:

1. stretch
2. compression
3. reflection in x-axis
4. horizontal translation
5. vertical translation
6. all transformations combined

Answer 8

1. f(x) = ax^2, when a > 1

2. f(x) = ax^2, when 0

Question 9

The form ax^2 +bx +c, where a does not equal zero, is referred to as what?

Answer 9

standard form

Question 10

What is the y-value of the vertex of any quadratic function that is written in standard form?

Answer 10

f ( -b/2a )

Question 11

What three points on the graph of a quadratic function.

Answer 11

Three noncollinear points, no two of which are in a line vertically, are on the graph of exactly one quadratic function.

Question 12

factoring

Answer 12

Re-writing an expression as the product of its factors.

Question 13

greatest common factor (GCF)

Answer 13

The common factor of each term of an expression that has the greatest coefficient and the greatest exponent.

Question 14

perfect square trinomial

Answer 14

A trinomial that is the square of a binomial.

Example:
Binomial Square = (4x - 3)^2
Trinomial = 16x^2 -24x +9

Question 15

difference of two squares

Answer 15

An expression of the form a^2 - b^2. It can be factored in the form (a + b)(a - b).

Question 16

zero of a function

Answer 16

Any number x for which f(x) = 0.

Question 17

zero-product property

Answer 17

For all numbers a and b, if ab = 0, then a = 0 or b = 0.

Question 18

completing the square

Answer 18

The process of finding a constant c to add to x^2 +bx so that x^2 +bx +c is the square of a binomial.