Quadratic Identities
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 6 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
- 6
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- 6
- Answered
- Review
-
Question 1 of 6
1. Question
Find the values of A, B and C, given that:x2+6x-2≡A(x+1)2+B(x+1)+C-
A= (1)B= (4)C= (-7)
Hint
Help VideoCorrect
Fantastic!
Incorrect
Need TextPlayCurrent Time 0:00/Duration Time 0:00Remaining Time -0:00Stream TypeLIVELoaded: 0%Progress: 0%0:00Fullscreen00:00MutePlayback Rate1x- 2x
- 1.5x
- 1.25x
- 1x
- 0.75x
- 0.5x
Subtitles- subtitles off
Captions- captions off
- English
Chapters- Chapters
Standard Form
ax2+bx+cA Quadratic Identity is composed of two quadratic equations that exactly match each other.First, list the coefficients of the quadratic equation on the left sidex2+6x-2a=1 b=6 c=-2Next, expand the right side of the identity and arrange it in standard formA(x+1)2+B(x+1)+C = A(x2+2x+1)+B(x+1)+C = Ax2+2Ax+A+Bx+B+C = Ax2+2Ax+Bx+A+B+C = Ax2+(2A+B)x+A+B+C Equate each corresponding coefficient to solve for A, B and CCoefficient of x2:Ax2+(2A+B)x+A+B+C1x2+6x-2A = 1 Coefficient of x:Ax2+(2A+B)x+A+B+Cx2+6x-22A+B = 6 2(1)+B = 6 Substitute A 2+B = 6 2+B -2 = 6 -2 Subtract 2 from both sides B = 4 Constants:Ax2+(2A+B)x+A+B+Cx2+6x-2A+B+C = -2 1+4+C = -2 Substitute A and B 5+C = -2 5+C -5 = -2 -5 Subtract 5 from both sides C = -7 A=1B=4C=-7 -
-
Question 2 of 6
2. Question
Find the values of A, B and C, given that:2x2+5x-2≡A(x+2)2+B(x+2)+C-
A= (2)B= (-3)C= (-4)
Hint
Help VideoCorrect
Excellent!
Incorrect
Need TextPlayCurrent Time 0:00/Duration Time 0:00Remaining Time -0:00Stream TypeLIVELoaded: 0%Progress: 0%0:00Fullscreen00:00MutePlayback Rate1x- 2x
- 1.5x
- 1.25x
- 1x
- 0.75x
- 0.5x
Subtitles- subtitles off
Captions- captions off
- English
Chapters- Chapters
Standard Form
ax2+bx+cA Quadratic Identity is composed of two quadratic equations that exactly match each other.First, list the coefficients of the quadratic equation on the left side2x2+5x-2a=2 b=5 c=-2Next, expand the right side of the identity and arrange it in standard formA(x+2)2+B(x+2)+C = A(x2+4x+4)+B(x+2)+C = Ax2+4Ax+4A+Bx+2B+C = Ax2+4Ax+Bx+4A+2B+C = Ax2+(4A+B)x+4A+2B+C Equate each corresponding coefficient to solve for A, B and CCoefficient of x2:Ax2+(4A+B)x+4A+2B+C2x2+5x-2A = 2 Coefficient of x:Ax2+(4A+B)x+4A+2B+C2x2+5x-24A+B = 5 4(2)+B = 5 Substitute A 8+B = 5 8+B -8 = 5 -8 Subtract 8 from both sides B = -3 Constants:Ax2+(4A+B)x+4A+2B+Cx2+5x-24A+2B+C = -2 4(2)+2(-3)+C = -2 Substitute A and B 8-6+C = -2 2+C -2 = -2 -2 Subtract 2 from both sides C = -4 A=2B=-3C=-4 -
-
Question 3 of 6
3. Question
Find the values of A, B and C, given that:-x2+5x-2≡A(x+3)2+B(x+3)+C-
A= (-1)B= (11)C= (-26)
Hint
Help VideoCorrect
Nice Job!
Incorrect
Need TextPlayCurrent Time 0:00/Duration Time 0:00Remaining Time -0:00Stream TypeLIVELoaded: 0%Progress: 0%0:00Fullscreen00:00MutePlayback Rate1x- 2x
- 1.5x
- 1.25x
- 1x
- 0.75x
- 0.5x
Subtitles- subtitles off
Captions- captions off
- English
Chapters- Chapters
Standard Form
ax2+bx+cA Quadratic Identity is composed of two quadratic equations that exactly match each other.First, list the coefficients of the quadratic equation on the left side-x2+5x-2a=-1 b=5 c=-2Next, expand the right side of the identity and arrange it in standard formA(x+3)2+B(x+3)+C = A(x2+6x+9)+B(x+3)+C = Ax2+6Ax+9A+Bx+3B+C = Ax2+6Ax+Bx+9A+3B+C = Ax2+(6A+B)x+9A+3B+C Equate each corresponding coefficient to solve for A, B and CCoefficient of x2:Ax2+(6A+B)x+9A+3B+C-1x2+5x-2A = -1 Coefficient of x:Ax2+(6A+B)x+9A+3B+C-x2+5x-26A+B = 5 6(-1)+B = 5 Substitute A -6+B = 5 -6+B +6 = 5 +6 Add 6 to both sides B = 11 Constants:Ax2+(4A+B)x+9A+3B+C-x2+5x-29A+3B+C = -2 9(-1)+3(11)+C = -2 Substitute A and B -9+33+C = -2 24+C -24 = -2 -24 Subtract 24 from both sides C = -26 A=-1B=11C=-26 -
-
Question 4 of 6
4. Question
Find the values of P, Q and R, given that:x2-3≡P(x-3)2+Q(x+1)-2R-
P= (1)Q= (6)R= (9)
Hint
Help VideoCorrect
Well Done!
Incorrect
Need TextPlayCurrent Time 0:00/Duration Time 0:00Remaining Time -0:00Stream TypeLIVELoaded: 0%Progress: 0%0:00Fullscreen00:00MutePlayback Rate1x- 2x
- 1.5x
- 1.25x
- 1x
- 0.75x
- 0.5x
Subtitles- subtitles off
Captions- captions off
- English
Chapters- Chapters
Standard Form
ax2+bx+cA Quadratic Identity is composed of two quadratic equations that exactly match each other.First, list the coefficients of the quadratic equation on the left sidex2-3a=1 b=0 c=-3Next, expand the right side of the identity and arrange it in standard formP(x-3)2+Q(x+1)-2R = P(x2-6x+9)+Q(x+1)-2R = Px2-6Px+9P+Qx+Q-2R = Px2-6Px+Qx+9P+Q-2R = Px2+(-6P+Q)x+9P+Q-2R Equate each corresponding coefficient to solve for P, Q and RCoefficient of x2:Px2+(-6P+Q)x+9P+Q-2R1x2-3P = 1 Coefficient of x:Px2+(-6P+Q)x+9P+Q-2Rx2-3-6P+Q = 0 -6(1)+Q = 0 Substitute P -6+Q = 0 -6+Q +6 = 0 +6 Add 6 to both sides Q = 6 Constants:Px2+(-6P+Q)x+9P+Q-2Rx2-39P+Q-2R = -3 9(1)+6-2R = -3 Substitute P and Q 15-2R = -3 15-2R -15 = -3 -15 Subtract 15 from both sides -2R÷(-2) = -18÷(-2) Divide both sides by -2 R = 9 P=1Q=6R=9 -
-
Question 5 of 6
5. Question
Find the values of P, Q and R, given that:2x2+5x-3≡Px(x-5)+(Qx-1)(R+1)-
P= (2)Q= (5)R= (2)
Hint
Help VideoCorrect
Great Work!
Incorrect
Need TextPlayCurrent Time 0:00/Duration Time 0:00Remaining Time -0:00Stream TypeLIVELoaded: 0%Progress: 0%0:00Fullscreen00:00MutePlayback Rate1x- 2x
- 1.5x
- 1.25x
- 1x
- 0.75x
- 0.5x
Subtitles- subtitles off
Captions- captions off
- English
Chapters- Chapters
Standard Form
ax2+bx+cA Quadratic Identity is composed of two quadratic equations that exactly match each other.First, list the coefficients of the quadratic equation on the left side2x2+5x-3a=2 b=5 c=-3Next, expand the right side of the identity and arrange it in standard formPx(x-5)+(Qx-1)(R+1) = Px2-5Px+QxR+Qx-R-1 = Px2+(-5P+QR+Q)x-R-1 Equate each corresponding coefficient to solve for P, Q and RCoefficient of x2:Px2+(-6P+Q)x+9P+Q-2R2x2+5x-3P = 2 Constants:Px2+(-5P+QR+Q)x-R-12x2+5x-3-R-1 = -3 -R-1 +1 = -3 +1 Add 1 to both sides -R÷(-1) = -2÷(-1) Divide both sides by -1 R = 2 Coefficient of x:Px2+(-5P+QR+Q)x-R-12x2+5x-3-5P+QR+Q = 5 -5P+Q(R+1) = 5 -5(2)+Q(2+1) = 5 Substitute P and R -10+3Q = 5 -10+3Q +10 = 5 +10 Add 10 to both sides 3Q÷3 = 15÷3 Divide both sides by 3 Q = 5 P=2Q=5R=2 -
-
Question 6 of 6
6. Question
Find the values of K, L and M, given that:9x2-6x+2≡(Kx-3)2+L(x-3)+M-
K= (3, -3) and (3, -3)L= (12, -24) and (12, -24)M= (29, -79) and (29, -79)
Hint
Help VideoCorrect
Keep Going!
Incorrect
Need TextPlayCurrent Time 0:00/Duration Time 0:00Remaining Time -0:00Stream TypeLIVELoaded: 0%Progress: 0%0:00Fullscreen00:00MutePlayback Rate1x- 2x
- 1.5x
- 1.25x
- 1x
- 0.75x
- 0.5x
Subtitles- subtitles off
Captions- captions off
- English
Chapters- Chapters
Standard Form
ax2+bx+cA Quadratic Identity is composed of two quadratic equations that exactly match each other.First, list the coefficients of the quadratic equation on the left side9x2-6x+2a=9 b=-6 c=2Next, expand the right side of the identity and arrange it in standard form(Kx-3)2+L(x-3)+M = K2x2-6Kx+9+Lx-3L+M = K2x2-6Kx+Lx+9-3L+M = K2x2+(-6K+L)x+9-3L+M Equate each corresponding coefficient to solve for A, B and CCoefficient of x2:K2x2+(-6K+L)x+9-3L+M9x2-6x+2K2 = 9 √K2 = √9 Take the square root of both sides K = ±3 K = 3 K = -3 Coefficient of x:K2x2+(-6K+L)x+9-3L+M9x2-6x+2Substitute K=3-6K+L = -6 -6(3)+L = -6 -18+L = -6 -18+L +18 = -6 +18 L = 12 Substitute K=-3-6K+L = -6 -6(-3)+L = -6 18+L = -6 18+L -18 = -6 -18 L = -24 Constants:K2x2+(-6K+L)x+9-3L+M9x2-6x+2Substitute L=129-3L+M = 2 9-3(12)+M = 2 9-36+M = 2 -27+M = 2 -27+M +27 = 2 +27 M = 29 Substitute L=-249-3L+M = 2 9-3(-24)+M = 2 9+72+M = 2 81+M = 2 81+M -81 = 2 -81 M = -79 K=3 and K=-3L=12 and L=-24M=29 and M=-79 -
Quizzes
- Sum & Product of Roots 1
- Sum & Product of Roots 2
- Sum & Product of Roots 3
- Sum & Product of Roots 4
- Solving Equations by Factoring 1
- Solving Equations Using the Quadratic Formula
- Completing the Square 1
- Completing the Square 2
- Intro to Quadratic Functions (Parabolas) 1
- Intro to Quadratic Functions (Parabolas) 2
- Intro to Quadratic Functions (Parabolas) 3
- Graph Quadratic Functions in Standard Form 1
- Graph Quadratic Functions in Standard Form 2
- Graph Quadratic Functions by Completing the Square
- Graph Quadratic Functions in Vertex Form
- Write a Quadratic Equation from the Graph
- Write a Quadratic Equation Given the Vertex and Another Point
- Quadratic Inequalities 1
- Quadratic Inequalities 2
- Quadratics Word Problems 1
- Quadratics Word Problems 2
- Quadratic Identities
- Graphing Quadratics Using the Discriminant
- Positive and Negative Definite
- Applications of the Discriminant 1
- Applications of the Discriminant 2
- Solving Reducible Equations