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Quadratic Inequalities 1Quadratic Inequalities 1
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Question 1 of 4
1. Question
Solve for `x``x^2x12≤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^2x12` `≤` `0` `x^2x12` `=` `0` `(x+3)(x4)` `=` `0` `x+3` `=` `0` `x+3` `3` `=` `0` `3` `x` `=` `2` `x4` `=` `0` `x4` `+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^2x12` `≤` `0` `(5)^2(5)12` `≤` `0` Substitute `x=5` `25+512` `≤` `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+3xx^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+3xx^2` `=` `0` `x^2+3x+4` `=` `0` Convert to standard form `x^23x4` `=` `0` Multiply the function by `1` `x^23x4` `=` `0` `(x4)(x+1)` `=` `0` `x4` `=` `0` `x4` `+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+3xx^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` axisThis 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^27x4` `=` `0` Convert to standard form `2x^27x4` `=` `0` `(2x+1)(x4)` `=` `0` `2x+1` `=` `0` `2x+1` `1` `=` `0` `1` `2x``divide2` `=` `1``divide2` `x` `=` `1/2` `x4` `=` `0` `x4` `+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^27x4` `y` `=` `2(0)^27(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` axisHence, `x``<``1/2` and `x``>``4``x``<``1/2` and `x``>``4` 
Question 4 of 4
4. Question
Solve for `x``5x^2+7x2≥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+7x2` `≥` `0` `5x^2+7x2` `=` `0` `(5x2)(x1)` `=` `0` `5x2` `=` `0` `5x2` `+2` `=` `0` `+2` `5x``divide5` `=` `2``divide5` `x` `=` `2/5` `x1` `=` `0` `x1` `+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+7x2` `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` axisHence, `2/5≤x≤1``2/5≤x≤1`
Quizzes
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 Graph Quadratic Functions in Standard Form 1
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 Quadratic Inequalities 1
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 Quadratic Identities
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 Positive and Negative Definite
 Applications of the Discriminant 1
 Applications of the Discriminant 2
 Combining Methods for Solving Quadratic Equations