Overview of Quadratic Functions

MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C84C72.B2E78840" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C84C72.B2E78840 Content-Location: file:///C:/AEC94292/SolutionsQuadraticFunctionRR.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Overview of Quadratic Functions

@ Solution of Quadratic Func= tion with Rational Roots @

A Quadratic Function is an Algebraic equation of two variables. One variable

is a second degree while the other is first then usually followed by a constant.

Graph or curve (Set of Pts) of a Quadratic Function resembles a U s= hape curve.

One variable is calle= d the independent variable = while the other is called the

<= span style=3D'color:blue;mso-bidi-font-weight:bold'>dependent variable. The independent is = the horizontal variable while the

d= ependent variable is the vertical variable. Use Gizmo to explore Quadratics!

Quadratic Functions (equations) normally appear in distinct arrangements:

= ; Standa= rd Form: f(x) =3D ax² + bx + c, A,B,C ar= e real numbers.

Other essential characteristics is that (a) is nonzero real number and f(x) =3D y

= ; also, (x) is considered the Domain (H va= lues) while (y) the = Range (V values).

If the Domain of X is real numbers then<= /span> a Quadratic Curve will cross the X axis twice.<= /p>

Locate: = Intercepts, Axis of Symmetry, Vertex, Symmetry Point to sketch solution!

Given: y=3D = +x² –x –6 Determine Infinite Solution Set which is a U s= haped curve!

Try to factor the Quadratic first to determine if it has Rational Roots or X intercepts!

Given: y =3D= x² –x –6 =3D (x – = 3) (x + 2) are factors thus = x =3D +3 & x =3D –2 Rational= Roots!

The (X) Intercepts are – 3 and + 2 while the (Y) Intercept is y =3D (= 0)² –(0) –6 =3D ̵= 1;6

Using the Midpoint Formula: ( X1 + X2) / 2 = =3D + 3 + – 2 =3D + 1/2 Axis of Symmetry!=

Substitute Midpoint to locate Vertex: y =3D= (+1/2)² – (+ 1/2) – 6 =3D += 1/4 – 1/2 – 6 =3D = 211; 6 1/4

= Thus: Vertex =3D ( +1/2 , – 6 1/4 ) Locate Symmetry Point by u= sing Axis of Symmetry!

Using Property of Symmetry and (Y) Intercept locate the Symmetry Point! Why?

Symmetry Point: y =3D x2 –x –6 =3D (– 1)² – (+ 1) – 6 =3D + (1) – (1) – 6 =3D – 6 (0,= – 6)!

The Infinite Solution Set of y =3D x² –x –6 equals Graph of y =3D x² &#= 8211;x –6 shown below!

X	-2	+3	0	+1	+ 1/2
Y	0	0	– 6	– 6	–= ; 6 1 /4

&nb= sp;

Tom Love = &nb= sp; Malone College = Fall 2007

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