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 ﻿ Chapter 10 Lesson 10-1 Exploring Quadratic Graphs Solving by Graphing Quadratic Function: y=ax²+bx+c

Here are some examples of this function written in standard form: y=2x² y=x²+7 y=-x²-3

When creating the graph, it will always make a U-shaped line, which is called a parabola. Here's easy steps to making your graphs on your graphing calculator: 1. Press the y= button. 2. Type in your functions. ex:y=2x² 3. Press the graph button. 4. There's your graph!

Here's a video if you're having trouble:[|Quadratic Graph Video]

 Going along with the Parabola is the Minimum, and Maximum point.

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%; line-height: 0px; overflow: hidden;">Here are the rules:

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%; line-height: 0px; overflow: hidden;">If in the function a <0, the parabola opens downward and the vertex is a maximum point, or the highest point of the parabola.

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%; line-height: 0px; overflow: hidden;">If in the function a>0, the parabola opens upward, and the vertex is a minimum point, or the lowest point of the parabola.

<span style="color: #db00ff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 200%; line-height: 0px; overflow: hidden;">10-2 Quadratic Functions

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%; line-height: 0px; overflow: hidden;">In this lesson we will be symplifying and graphing functions.

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%; line-height: 0px; overflow: hidden;">There are <span style="color: #00ddff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%; line-height: 0px; overflow: hidden;">4 easy steps to graphing a function:

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%; line-height: 0px; overflow: hidden;"><span style="color: #00ddff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%; line-height: 0px; overflow: hidden;">Step 1- What is the axis of symmetry?

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%; line-height: 0px; overflow: hidden;">x=-b/2a

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">y=2x²+4x-3 -(4)/2(2) -4/4= -1 <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">Make a dotted line on your graph at -1.

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%; line-height: 0px; overflow: hidden;"><span style="color: #00ddff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%; line-height: 0px; overflow: hidden;">Step 2- What is the vertex?

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%; line-height: 0px; overflow: hidden;">Take the axis of symmetry, and plug it into the function.

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">y=2(-1)²+4(-1)-3 y=2(1)-4-3 y=-5 <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">Make a dot on the axis of symmetry at -5, or point (-1,-5) and on the other side of the axis of symmetry.

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;"><span style="color: #00ddff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">Step 3- What is the y-intercept? <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">Plug 0 into the function. <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">y=2(0)²+4(0)-3 y=0+0-3 y=-3 <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">Plot a point on (0,-3) and on the other side of the axis of symmetry which is (-2,-3).

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;"><span style="color: #00ddff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">Step 4- One more point! <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">Figure out one more point to plot, picking 1 is easy. <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">y=2(1)²+4(1)-3 y=2(1)+4-3 y=2+1 y=3 <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">Plot one more point on (1,3) and on the other side of the axis of symmetry which is (-3,3).

<span style="color: #ffac00; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 190%;">10-3 Solving Quadratic Equations <span style="color: #ffac00; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 190%;">Solve by square roots

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">Solve <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">2x²-98=0 <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">First, add 98 to both sides. <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">2x²=98 <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">Then divide both sides by 2 to get x² by itself. <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">x²=49 <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">Next find the square roots. <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">√x²=√49 <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">x=7

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">You can now solve quadratic equations three different ways! By graphing on your calculater, finding the intercepts, and solving by square roots. Here's some review! <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">[|Lesson Quiz 1]

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">[|Lesson Quiz 2]

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 140%;">[|Lesson Quiz 3]