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Quadratic Inequalities 1Quadratic Inequalities 1
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Question 1 of 4
1. Question
Solve for `x``x^2-x-12≤0`Hint
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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
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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
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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
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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