Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

Objective: In this lesson you learned how to sketch and analyze graphs

Important Vocabulary Define each term or concept.

Constant function A polynomial function with degree 0. That is, f(x) = a, a ≠ 0.
Linear function A polynomial function with degree 1. That is, f(x) = mx + b, m ≠ 0.
Quadratic function Let a, b, and c be real numbers with a ≠ 0. The function f(x) =
ax2 + bx + c is called a quadratic function.
Axis of symmetry A line about which a parabola is symmetric. Also called simply
the axis of the parabola.
Vertex The point where the axis intersects the parabola.

I. The Graph of a Quadratic Function (Pages 136-138)

Let n be a nonnegative integer and let be
real numbers with A polynomial function of x with
degree n is . . .

the function

What you should learn
How to analyze graphs of

A quadratic function is a polynomial function of second
degree. The graph of a quadratic function is a special “U”-shaped
curve called a parabola .

graph of the function opens upward and the vertex of
the parabola is the minimum point on the graph. If the
of the function opens downward and the vertex of the
parabola is the maximum point on the graph.

II. The Standard Form of a Quadratic Function
(Pages 139-140)

The standard form of a quadratic function is

For a quadratic function in standard form, the axis of the
associated parabola is x = h and the vertex is
(h, k) .

What you should learn
functions in standard
form and use the results
to sketch graphs of
functions

To write a quadratic function in standard form , . . . use the
process of completing the square on the variable x.

To find the x-intercepts of the graph of f (x) = ax2 + bx + c , . . .
solve the equation ax2 + bx + c = 0.

Example 1: Sketch the graph of f (x) = x2 + 2x - 8 and
identify the vertex, axis, and x-intercepts of the
parabola.
(- 1, - 9); x = - 1; (- 4, 0) and (2, 0)

III. Applications (Pages 141-142)
For a quadratic function in the form f (x) = ax2 + bx + c , when
a > 0, f has a minimum that occurs at - b/(2a) .
When a < 0, f has a maximum that occurs at - b/(2a) .
To find the minimum or maximum value, evaluate the
function at - b/(2a) .

What you should learn