Solving Quadratics by Graphing -...
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GSE Algebra I Solving Quadratics Notes Name: Date: A (equation is any equation having the form C A quadratic funchon forms a graph called a (shaped like a u). In this unit, we will solve quadratic equations, meaning we will find the values of xwhen y= O. Solving Quadratics by Graphing Solve a quadratic by Graphinq To solve a quadratic by graphing is to find where the parabola crosses the ) 3 We call these the solutions roots zeros or x-intercepts. Example 1: Find the zeros. You try: Find the solutions. (L/ IUD Practice: Identify the solutions of each quadratic graph. 78 9 10
Transcript of Solving Quadratics by Graphing -...
GSE Algebra I Solving Quadratics Notes
Name: Date:A (equation is any equation having the form C A quadratic
funchon forms a graph called a (shaped like a u).In this unit, we will solve quadratic equations, meaning we will find the values of xwhen y= O.
Solving Quadratics by Graphing
Solve a quadratic by GraphinqTo solve a quadratic by graphing is to find where the parabola crosses the ) 3
We call these the solutions roots zeros or x-intercepts.
Example 1: Find the zeros. You try: Find the solutions.
(L/ IUD
Practice: Identify the solutions of each quadratic graph.
78 9 10
—Solve by Factoring Notes—
o The -ZLLL Product Property is used to solve an equation when one side is zero and theother side is a product of polynomial factorso For xample: m •n = 0, then m = 0 or n = 0. The solutions of such an equation are alsocalled
Example:
X-3=O or x +6=0
The solutions(roots) of the equation are 3 and - 6
Exam les: Solve.
5. x(x-5) 6. 2x(3x+ l)
21 4
Factor usin GCF. Then solve.7. + 12x=o 8. 14x=0 10. 0
x (1+14) — o
14-
Factor usin DOTS. Then solve11. p2 -36=O 13.
( P—lp) > O
Factor each trinomial. Then solve.14. + -28 = o 15. x2 +x-42=o 16. +81 8)21
10/-7
18. -o 19. x2 +2x-
( 1+uEO21-1
3 (1-13
2
Algebra I Name
Solving by Factoring Practice
o Solve each equation.
5) (4x4 1) -o
CFactor using GCF. Then solve.
9) x2 + 6x = 0
11) -2x=o
10) 3x2 +24x=o
12) 7x2 -21x=o
Factor using DOTS. Then solve.
13) x2 -25=0 14) -9=0
3
15) 64x2 —49 = 0 16) 25x2 - 16=0
o
6)
Solve each equation by factoring.
17) x2ー1 Ox + 24 = 0 ) x2 ーx ー20 = 0
( Y ) (レ ルの の(x + 4 )フ0
乂ン4 /ニ し
1 9) x2 ー2x ー48 = 0 20 ) x2ー6x + 8 = 0
デ銧x +レ)ン〇 (ー の似っル0
こ8 /ーし Kごな/ /ラ乙
21 ) x2 + 5x ーヨ4 = 0 22 ) x2 + 3x ー40 = 0
0
びーx 十つニD ( xーっ(ナ&ル0
23 ) x2 + 2x ー3 = 0 24 ) x2 + 7x + 10 = 0
(乂丑の 保—))プ0 を+り( xサプ の
メ= ー3 /メ こ/
Solve eac tion by factoring (Bottoms Up).
25 ) 5X2 ー19X ー4 = 0 20 26 ) 7X2 + 15x + 8 = 0い乙0 のフ
秋 ーK ゼ ) =の (x ) ( x ル の
Cの 々担ル0 乙和上び刊レD ー 一ノ乂= &ん27) x2ー7x 28) 5ェ2 + 12X + 4 = 0 レ 0
どYー秋 ル ℃ +ナ し 0( ← xール 0 は刊) (K+を ) = 0
29) 行, 7 読 之0 30) 4x ー15Xー= 0
区坦 なザ= 0 ( x + Dは一
7フ( K垣 )びサ/ ) = 0 )に の = 0
引) 2X2 + 13X 1 = 32) 10X2ー9x + 2レ 0
0 )は+しレ0 220
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