Topics
>
Algebra 1>
Quadratic Equations and Functions>
Quadratic Inequalities>
Quadratic Inequalities 1Quadratic Inequalities 1
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 4 questions completed
Questions:
- 1
- 2
- 3
- 4
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
- Answered
- Review
-
Question 1 of 4
1. Question
Solve for `x``x^2-x-12≤0`Hint
Help VideoCorrect
Great Work!
Incorrect
Representing Inequalities on the Number Line
Greater than (`>`)
Greater than or equal (`≥`)
Less than (`<`)
Less than or equal (`≤`)
First, change the inequality sign into an equal sign and find the `x` values using cross method`x^2-x-12` `≤` `0` `x^2-x-12` `=` `0` 
`(x+3)(x-4)` `=` `0` `x+3` `=` `0` `x+3` `-3` `=` `0` `-3` `x` `=` `-2` `x-4` `=` `0` `x-4` `+4` `=` `0` `+4` `x` `=` `4` Mark these `2` points on a number plane. Use filled dots since the sign used is `≤`
Next, test a point to determine which part of the number line is covered by `x`Try `x=-5``x^2-x-12` `≤` `0` `(-5)^2-(-5)-12` `≤` `0` Substitute `x=-5` `25+5-12` `≤` `0` `18` `≤` `0` This is not true, which means `-3≤x≤4`
`-3≤x≤4` -
Question 2 of 4
2. Question
Solve for `x``4+3x-x^2≥0`Hint
Help VideoCorrect
Correct!
Incorrect
The cross method is a factorisation method used for quadratics.First, change the inequality sign into an equal sign and find the `x` values using cross method`4+3x-x^2` `=` `0` `-x^2+3x+4` `=` `0` Convert to standard form `x^2-3x-4` `=` `0` Multiply the function by `-1` `x^2-3x-4` `=` `0` 
`(x-4)(x+1)` `=` `0` `x-4` `=` `0` `x-4` `+4` `=` `0` `+4` `x` `=` `4` `x+1` `=` `0` `x+1` `-1` `=` `0` `-1` `x` `=` `-1` Mark these `2` points on the `x` axis.
Next, substitute `x=0` to the function to get the `y` intercept`y` `=` `4+3x-x^2` `y` `=` `4+3(0)-(0)^2` Substitute `x=0` `y` `=` `4` Mark this point on the `y` axis.
Form a parabola by connecting the pointsSince we are looking for `y≥0`, the values are on or above the `x` axis
This means that `x` is greater than or equal to `-1` and less than or equal to `4``-1≤x≤4` -
Question 3 of 4
3. Question
Solve for `x``2x^2>7x+4`Hint
Help VideoCorrect
Keep Going!
Incorrect
The cross method is a factorisation method used for quadratics.First, change the inequality sign into an equal sign and find the `x` values using cross method`2x^2` `=` `7x+4` `2x^2-7x-4` `=` `0` Convert to standard form `2x^2-7x-4` `=` `0` 
`(2x+1)(x-4)` `=` `0` `2x+1` `=` `0` `2x+1` `-1` `=` `0` `-1` `2x``divide2` `=` `-1``divide2` `x` `=` `-1/2` `x-4` `=` `0` `x-4` `+4` `=` `0` `+4` `x` `=` `4` Mark these `2` points on the `x` axis.
Next, substitute `x=0` to the function to get the `y` intercept`y` `=` `2x^2-7x-4` `y` `=` `2(0)^2-7(0)-4` Substitute `x=0` `y` `=` `-4` Mark this point on the `y` axis.
Form a parabola by connecting the pointsSince we are looking for `y``>``0`, the values are above the `x` axis
Hence, `x``<``-1/2` and `x``>``4``x``<``-1/2` and `x``>``4` -
Question 4 of 4
4. Question
Solve for `x``-5x^2+7x-2≥0`Hint
Help VideoCorrect
Fantastic!
Incorrect
The cross method is a factorisation method used for quadratics.First, change the inequality sign into an equal sign and find the `x` values using cross method`-5x^2+7x-2` `≥` `0` `-5x^2+7x-2` `=` `0` 
`(5x-2)(x-1)` `=` `0` `5x-2` `=` `0` `5x-2` `+2` `=` `0` `+2` `5x``divide5` `=` `2``divide5` `x` `=` `2/5` `x-1` `=` `0` `x-1` `+1` `=` `0` `+1` `x` `=` `1` Mark these `2` points on the `x` axis.
Next, substitute `x=0` to the function to get the `y` intercept`y` `=` `-5x^2+7x-2` `y` `=` `-5(0)^2+7(0)-2` Substitute `x=0` `y` `=` `-2` Mark this point on the `y` axis.
Form a parabola by connecting the pointsSince we are looking for `y≥0`, the values are above the `x` axis
Hence, `2/5≤x≤1``2/5≤x≤1`
Quizzes
- Solve Quadratics by Factoring
- 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
- Combining Methods for Solving Quadratic Equations