Years
>
Year 11>
Quadratic Polynomial>
Graphing Quadratics Using the Discriminant>
Graphing Quadratics Using the DiscriminantGraphing Quadratics Using the Discriminant
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 7 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
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
- 7
- Answered
- Review
-
Question 1 of 7
1. Question
Which of the following graphs have a discriminant that is equal to 0?
(Δ=0)- 1.
-
2.
-
3.
-
4.
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
Nature of the Roots Discriminant (Δ) Two real roots Δ>0 One real root Δ=0 No real roots Δ<0 Discriminant Formula
Δ=b2−4acFor each graph, check how many times the graph has passed through the x axisThis graph touched the x axis once, which means it has one rootHence, Δ=0This graph touched the x axis twice, which means it has two rootsHence, Δ>0This graph touched the x axis once, which means it has one rootHence, Δ=0This graph touched the x axis twice, which means it has two rootsHence, Δ>0 -
Question 2 of 7
2. Question
Which function does not intersect with the x axis?-
1.
-
2.
-
3.
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
Nature of the Roots Discriminant (Δ) Two real roots Δ>0 One real root Δ=0 No real roots Δ<0 Discriminant Formula
Δ=b2−4acCompute for the discriminant of each functionx2-4x+3=0a=1 b=-4 c=3Δ = b2−4ac Discriminant Formula = (−4)2−4(1)(3) Substitute values = 16-12 = 4 Since Δ>0, this function has two real roots and intersects the x axis twicex2-4x+4=0a=1 b=-4 c=4Δ = b2−4ac Discriminant Formula = (−4)2−4(1)(4) Substitute values = 16-16 = 0 Since Δ=0, this function has one real root and intersects the x axis oncex2-4x+5=0a=1 b=-4 c=5Δ = b2−4ac Discriminant Formula = (−4)2−4(1)(5) Substitute values = 16-20 = -4 Since Δ<0, this function has no real roots and does not intersect the x axisx2-4x+5=0 -
1.
-
Question 3 of 7
3. Question
Graph using the discriminanty=2x2-2x-5-
1.
-
2.
-
3.
-
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
Quadratic Formula
x=−b±√Δ2aDiscriminant Formula
Δ=b2−4acFirst, compute for the discriminanty=2x2-2x-5a=2 b=-2 c=-5Δ = b2−4ac Discriminant Formula = −22−4(2)(−5) Substitute values = 4+40 = 44 Next, substitute the discriminant to the Quadratic Formula to find the x interceptsx = −b±√Δ2a Quadratic Formula = −(−2)±√442(2) Substitute values = 2±2√114 = 1±√112 Write each root individuallyx1 = 1+√112 = 2.158 x1 = 1-√112 = −1.158 Mark these 2 points on the x axisFind the y intercept by substituting x=0y = 2x2-2x-5 = 2(0)2-2(0)-5 Substitute x=0 = 0-0-5 = -5 Mark this on the y axisFinally, form the parabola by connecting the points -
1.
-
Question 4 of 7
4. Question
Graph using the discriminanty=3x2-4x-4-
1.
-
2.
-
3.
-
4.
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
Quadratic Formula
x=−b±√Δ2aDiscriminant Formula
Δ=b2−4acFirst, compute for the discriminanty=3x2-4x-4a=3 b=-4 c=-4Δ = b2−4ac Discriminant Formula = −42−4(3)(−4) Substitute values = 16+48 = 64 Next, substitute the discriminant to the Quadratic Formula to find the x interceptsx = −b±√Δ2a Quadratic Formula = −(−4)±√642(3) Substitute values = 4±86 Write each root individuallyx1 = 4+86 = 126 = 2 x1 = 4-86 = -46 = -23 Mark these 2 points on the x axisFind the y intercept by substituting x=0y = 3x2-4x-4 = 3(0)2-4(0)-4 Substitute x=0 = 0-0-4 = -4 Mark this on the y axisFinally, form the parabola by connecting the points -
1.
-
Question 5 of 7
5. Question
Graph using the discriminanty=2x2+3x-1-
1.
-
2.
-
3.
-
4.
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
Quadratic Formula
x=−b±√Δ2aDiscriminant Formula
Δ=b2−4acFirst, compute for the discriminanty=2x2+3x-1a=2 b=3 c=-1Δ = b2−4ac Discriminant Formula = 32−4(2)(−1) Substitute values = 9+8 = 17 Next, substitute the discriminant to the Quadratic Formula to find the x interceptsx = −b±√Δ2a Quadratic Formula = −3±√172(2) Substitute values = -3±√174 Write each root individuallyx1 = -3+√174 = 1.1234 = 0.281 x1 = -3-√174 = -7.1234 = -1.781 Mark these 2 points on the x axisFind the y intercept by substituting x=0y = 2x2+3x-1 = 2(0)2+3(0)-1 Substitute x=0 = 0+0-1 = -1 Mark this on the y axisFinally, form the parabola by connecting the points -
1.
-
Question 6 of 7
6. Question
Graph using the discriminanty=x2-6x+9-
1.
-
2.
-
3.
-
4.
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
Quadratic Formula
x=−b±√Δ2aAxis of Symmetry
x=−b2aDiscriminant Formula
Δ=b2−4acFirst, find the axis of symmetryy=x2-6x+9a=1 b=-6 c=9x = −b2a Axis of Symmetry x = −(−6)2(1) Substitute values x = 62 x = 3 Find where the graph touches the axis of symmetry by substituting x=3 to the function. This would be the vertexy = x2-6x+9 = (3)2-6(3)+9 Substitute x=3 = 9-18+9 = 0 Hence, the vertex is at (3,0)Next, compute for the discriminantΔ = b2−4ac Discriminant Formula = −62−4(1)(9) Substitute values = 36-36 = 0 Substitute the discriminant to the Quadratic Formula to find the x interceptsx = −b±√Δ2a Quadratic Formula = −(−6)±√02(1) Substitute values = 6±02 = 62 = 3 There is only one root or x intercept which is at (3,0)Recall that the (3,0) is also the vertexFind the y intercept by substituting x=0y = x2-6x+9 = (0)2-6(0)+9 Substitute x=0 = 0-0+9 = 9 Mark this on the y axisFinally, form the parabola by connecting the points -
1.
-
Question 7 of 7
7. Question
Graph using the discriminanty=x2+2x-8-
1.
-
2.
-
3.
-
4.
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
Quadratic Formula
x=−b±√Δ2aAxis of Symmetry
x=−b2aDiscriminant Formula
Δ=b2−4acFirst, find the axis of symmetryy=x2+2x-8a=1 b=2 c=-8x = −b2a Axis of Symmetry x = −22(1) Substitute values x = -22 x = -1 Find where the graph touches the axis of symmetry by substituting x=3 to the function. This would be the vertexy = x2+2x-8 = (-1)2+2(-1)-8 Substitute x=-1 = 1-2-8 = -9 Hence, the vertex is at (-1,-9)Next, compute for the discriminantΔ = b2−4ac Discriminant Formula = −22−4(1)(−8) Substitute values = 4+32 = 36 Substitute the discriminant to the Quadratic Formula to find the x interceptsx = −b±√Δ2a Quadratic Formula = −2±√362(1) Substitute values = -2±62 = -1±3 = -1-3,-1+3 x = -4,2 Finally, form the parabola by connecting the points -
1.
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