Standard Form
| Site: | Clare-Gladwin RESD |
| Course: | Michigan Algebra I |
| Book: | Standard Form |
| Printed by: | Guest user |
| Date: | Wednesday, January 15, 2025, 3:36 PM |
Description
Standard Form
Introduction
The standard form of a quadratic equation is ax2 + bx + c = 0 where a, b, and c are real numbers and a
0. Earlier in this unit, vertex form and factored form were discussed. There is a similarity between all three forms. The "a" in the standard form is the same "a" as in the factored and vertex form. That is, the a will always have exactly the same value. To determine the values of a, b, and c, write the equation in standard form.
Example 1 Find the a, b, and c values of the equation: x2 - 3x = 28.
Step 1. Put the equation in standard form.
1x2 - 3x - 28 = 0
Step 2. Identify the a, b, and c values.
a = 1, b = -3, c = -28
Example 2 Find the a, b, and c values of the equation: 5x2 = -45.
Step 1. Put the equation in standard form.
5x 2 + 0x + 45 = 0
Step 2. Identify the a, b, and c values.
a = 5, b = 0, c = 45
Exploration Activity
Investigating Standard Form ActivityAnswer Key
Standard Form Exploration Activity Answer Key
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Guided Practice
To solidify your understanding of graphing quadratic equations in standard form, visit the following link to Holt, Rinehart and Winston Homework Help Online. It provides examples, video tutorials and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.Guided Practice
Practice
Standard Form Graphing WorksheetAnswer Key
Standard From Graphing Answer KeyStandard to Vertex Form
Converting from standard to vertex form can be done by finding the x-and y- coordinates of the vertex. The formula for finding the x-coordinate of the vertex is
. The x-coordinate is used to find y and the "a" values are the same.
Example Rewrite y = 3x2 - 6x + 7 in vertex form.
Step 1. Find the x-coordinate of the vertex.
Step 2. Find the y-coordinate of the vertex.
Step 3. Rewrite the equation in vertex form.
Completing the Square
It is also possible to convert standard form to vertex form by completing the square. Completing the square was discussed in an earlier lesson. Now, apply the process to conversion.Example Convert y = x2 + 4x - 7 to vertex form.
In this equation, a = 1.
Step 3. Add the constant that will create a perfect square trinomial to each side.
Step 4. Factor and simplify.
Practice
Converting Standard to Vertex Form WorksheetAnswer Key
Converting Standard to Vertex Form Answer KeySources
Coffman, Joseph. "Translating Parabolas." http://www.jcoffman.com/Algebra2/ch5_3.htm (accessed 07/25/2010).
Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project
Holt, Rinehart & Winston, "Quadratic Functions and Equations ." http://my.hrw.com/math06_07/nsmedia/homework_help/alg1/alg1_ch09_03_homeworkhelp.html (accessed 8/22/2010).
Kuta Software, "Free Algebra 2 Worksheets." http://www.kutasoftware.com/freeia2.html (accessed 08/05/2010).