Page 565 - Algebra 1

L E S S O N Identifying Quadratic Functions 84
Warm Up
1. Vocabulary The equation f(x) = 7x2 - 3x + 1 is written in
(25)
(expanded, function) notation. Evaluate.
2. 6x3 for x = 2 (9)
4.500-7x2 forx=-10 (9)
5.Multiple_Choice Solve7x-y=2+6xfory. (29) 7x - 2
Ay= 6 B y=x-2 C y=-x
3. x2 - 4x + 3 for x = -3 (9)
D y=13x+2
New Concepts
A function pairs each value in the domain with exactly one value in the range. A quadratic function is a function that can be written in the form
f(x) = ax2 + bx + c, where a is not equal to 0. So, quadratic functions must have a quadratic term, but they may also have a linear and/or a constant term.
f(x) = ax2 + bx + c, where a ≠ 0
Math Language
The table shows ways to describe the domain and range.
Domain
Range
x-values
y-values
Independent variable
Dependent variable
x
f(x)
constant term linear term term
All quadratic functions consist of a polynomial expression with a degree of exactly 2. The degree of a polynomial is the same as the term with the greatest degree. The polynomial can be named by its highest degree.
A quadratic function can be written in many ways; however, there is a standard way to write a quadratic function.
If a function cannot be written in the standard form of a quadratic function, then the function is not quadratic.
quadratic
Polynomial
Degree
Name Using Degree
3x + 2
1
Linear
x2 +4x-5
2
Quadratic
2x3 -x2 +1
3
Cubic
Math Language
Quadratic comes from the Latin word quadratus, which means “square.”
Standard Form of a Quadratic Function
The standard form of a quadratic function is f(x) = ax2 + bx + c, where a, b, and c are real numbers and a ≠ 0.
550 Saxon Algebra 1