Years
>
Year 11>
Quadratic Polynomial>
Positive and Negative Definite>
Positive and Negative DefinitePositive and Negative Definite
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 5 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
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
- Answered
- Review
-
Question 1 of 5
1. Question
Which of the following graphs is a negative definite?Hint
Help VideoCorrect
Great Work!
Incorrect
Positive Definite
`Delta``<``0` and `a``>``0`A Positive Definite is a function that is always positive for all values of `x`. It is also a parabola that is concave up and is above the `x` axisNegative Definite
`Delta``<``0` and `a``<``0`A Negative Definite is a function that is always negative for all values of `x`. It is also a parabola that is concave down and is below the `x` axisCheck the characteristics of each graph to identify which is a Negative Definite
This parabola is concave up and is above the `x` axisTherefore, it is a Positive Definite
This parabola is concave down and is below the `x` axisTherefore, it is a Negative Definite
-
Question 2 of 5
2. Question
Identify whether the function below is a Negative Definite`y=-2x^2+2x-1`Hint
Help VideoCorrect
Correct!
Incorrect
Negative Definite
`Delta``<``0` and `a``<``0`Discriminant Formula
$$\Delta={\color{#9a00c7}{b}}^2-4\color{#00880A}{a}\color{#007DDC}{c}$$A Negative Definite is a function that is always negative for all values of `x`. It is also a parabola that is concave down and is below the `x` axisFirst, compute for the discriminant`y=-2x^2+2x-1``a=-2` `b=2` `c=-1``Delta` `=` $${\color{#9a00c7}{b}}^2-4\color{#00880A}{a}\color{#007DDC}{c}$$ Discriminant Formula `=` $${\color{#9a00c7}{2}}^2-4\color{#00880A}{(-2)}\color{#007DDC}{(-1)}$$ Substitute values `=` `4-8` `=` `-4` The value is negative, hence `Delta``<``0`Next, check the value of `a``y=``-2``x^2+2x-1``a=-2`The value is negative, hence `a``<``0`Therefore, we have established that the function is a Negative Definite -
Question 3 of 5
3. Question
Identify whether the function below is a Positive Definite`2x^2-x+3>0`Hint
Help VideoCorrect
Keep Going!
Incorrect
Positive Definite
`Delta``<``0` and `a``>``0`Discriminant Formula
$$\Delta={\color{#9a00c7}{b}}^2-4\color{#00880A}{a}\color{#007DDC}{c}$$A Positive Definite is a function that is always positive for all values of `x`. It is also a parabola that is concave up and is above the `x` axisFirst, compute for the discriminant`2x^2-x+3``a=2` `b=-1` `c=3``Delta` `=` $${\color{#9a00c7}{b}}^2-4\color{#00880A}{a}\color{#007DDC}{c}$$ Discriminant Formula `=` $${\color{#9a00c7}{-1}}^2-4\color{#00880A}{(2)}\color{#007DDC}{(3)}$$ Substitute values `=` `1-24` `=` `-23` The value is negative, hence `Delta``<``0`Next, check the value of `a``y=``2``x^2-x+3``a=2`The value is positive, hence `a``>``0`Therefore, we have established that the function is a Positive Definite -
Question 4 of 5
4. Question
For which values of `k` will the function below be a Positive Definite`y=kx^2+2kx+9`Hint
Help VideoCorrect
Fantastic!
Incorrect
Positive Definite
`Delta``<``0` and `a``>``0`Discriminant Formula
$$\Delta={\color{#9a00c7}{b}}^2-4\color{#00880A}{a}\color{#007DDC}{c}$$A Positive Definite is a function that is always positive for all values of `x`. It is also a parabola that is concave up and is above the `x` axisFirst, compute for the discriminant`y=kx^2+2kx+9``a=k` `b=2k` `c=9``Delta` `=` $${\color{#9a00c7}{b}}^2-4\color{#00880A}{a}\color{#007DDC}{c}$$ Discriminant Formula `=` $${\color{#9a00c7}{2k}}^2-4\color{#00880A}{(k)}\color{#007DDC}{(9)}$$ Substitute values `=` `4k^2-36k` Remember that for a function to be a Positive Definite, `Delta``<``0`Substitute the `Delta` computed previously, and then solve for `k``Delta` `<` `0` `4k^2-36k` `<` `0` `4k(k-9)` `<` `0` `k=0` `k=9` To determine which region around `k=0` and `k=9` would be included, plot these points and make a rough sketch of `4k^2-36k`Replace the `x` axis with `k` axis and draw an upward parabola since `4` is positive
Remember that `Delta` must be negativeTherefore, `0``<``k``<``9``0``<``k``<``9` -
Question 5 of 5
5. Question
For which values of `m` will the function below be a Positive Definite`mx^2+4mx+16`Hint
Help VideoCorrect
Excellent!
Incorrect
Positive Definite
`Delta``<``0` and `a``>``0`Discriminant Formula
$$\Delta={\color{#9a00c7}{b}}^2-4\color{#00880A}{a}\color{#007DDC}{c}$$A Positive Definite is a function that is always positive for all values of `x`. It is also a parabola that is concave up and is above the `x` axisFirst, compute for the discriminant`mx^2+4mx+16``a=m` `b=4m` `c=16``Delta` `=` $${\color{#9a00c7}{b}}^2-4\color{#00880A}{a}\color{#007DDC}{c}$$ Discriminant Formula `=` $${\color{#9a00c7}{4m}}^2-4\color{#00880A}{(m)}\color{#007DDC}{(16)}$$ Substitute values `=` `16m^2-64m` Remember that for a function to be a Positive Definite, `Delta``<``0`Substitute the `Delta` computed previously, and then solve for `m``Delta` `<` `0` `16m^2-64m` `<` `0` `16m(m-4)` `<` `0` `m=0` `m=4` To determine which region around `m=0` and `m=4` would be included, plot these points and make a rough sketch of `16m^2-64m`Replace the `x` axis with `m` axis and draw an upward parabola since `16` is positive
Remember that `Delta` must be negativeTherefore, `0``<``m``<``4``0``<``m``<``4`
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