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Why is this concept useful?: We use this concept in high school algebra, it can provide us information about what’s on either side of zero (positives and negatives).
Where does this concept fit into the curriculum?: High School

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How can we use the concept:

Quadratic inequalities can be solved by the factorization method or by using the quadratic formula.

Quadratic formula: x =

\frac{-b ± \sqrt(b^2-4ac)}{2a}

Steps to solve.

Step 1: Write the quadratic inequality in standard form:

ax^{2}

+ bx + c where a, b and are coefficients and a ≠ 0.

Step 2: Determine the roots of the inequality. In quadratic inequalities, these can also be called critical values.

Step 3: Write the solution in inequality notation or interval notation. If the quadratic inequality is in the form: (x – a) (x – b) ≥ 0, then a ≤ x ≤ b, and if it is in the form :(x – a) (x – b) ≤ 0, when a < b then a ≤ x or x ≥ b.

You can also use a graph to identify the solution set of the inequality.

Sample Math Problems

Question

x^{2}-2x-3 < 0

KaTeX can only parse string typed expression

Answer

Step 1: Write the quadratic inequality in standard form:

ax^2

+ bx + c where a, b and are coefficients and a ≠ 0.

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Practice Math Problems

1.

x^{2}

- 8x - 16 > 0

2.

x^{2}

< -9x - 14

3. 25 + 10x ≥ -

x^{2}

4.

x^{2}

- x - 12 ≤ 0

This step is complete.

Step 2: Determine the roots of the inequality. In quadratic inequalities, these can also be called critical values.

(x - 3)(x + 1) < 0

Step 3: Write the solution in inequality notation or interval notation. If the quadratic inequality is in the form: (x – a) (x – b) ≥ 0, then a ≤ x ≤ b, and if it is in the form :(x – a) (x – b) ≤ 0, when a < b then a ≤ x or x ≥ b.

-1 < x < 3

Question

x^{2}

+ 5x + 6 ≥ 0

Answer

Step 1: Write the quadratic inequality in standard form:

ax^{2}

+ bx + c where a, b and are coefficients and a ≠ 0.

This step is completed.

Step 2: Determine the roots of the inequality. In quadratic inequalities, these can also be called critical values.

x^{2}

+ 5x + 6 ≥ 0

(x + 3)(x + 2) ≥ 0

Step 3: Write the solution in inequality notation or interval notation. If the quadratic inequality is in the form: (x – a) (x – b) ≥ 0, then a ≤ x ≤ b, and if it is in the form :(x – a) (x – b) ≤ 0, when a < b then a ≤ x or x ≥ b.

-3 < x < -2

Question

x^{2}

< -7x - 10

Answer

Step 1: Write the quadratic inequality in standard form:

ax^{2}

+ bx + c where a, b and are coefficients and a ≠ 0.

x^{2}

+ 7x + 10 < 0

Step 2: Determine the roots of the inequality. In quadratic inequalities, these can also be called critical values.

(x + 2)(x + 5) < 0

Step 3: Write the solution in inequality notation or interval notation. If the quadratic inequality is in the form: (x – a) (x – b) ≥ 0, then a ≤ x ≤ b, and if it is in the form :(x – a) (x – b) ≤ 0, when a < b then a ≤ x or x ≥ b.

You can also use a graph to identify the solution set of the inequality.

x < -2 or x < -5

Question

x^{2}

- 11x + 30 ≤ 0

Answer

Step 1: Write the quadratic inequality in standard form:

ax^{2}

+ bx + c where a, b and are coefficients and a ≠ 0.

This step is completed.

Step 2: Determine the roots of the inequality. In quadratic inequalities, these can also be called critical values.

(x - 5)(x - 6) ≤ 0

Step 3: Write the solution in inequality notation or interval notation. If the quadratic inequality is in the form: (x – a) (x – b) ≥ 0, then a ≤ x ≤ b, and if it is in the form :(x – a) (x – b) ≤ 0, when a < b then a ≤ x or x ≥ b.

You can also use a graph to identify the solution set of the inequality.

x ≥ 5 or x ≥ 6

Download

Functions Worksheets

Quadratic Inequalities

Related Topics

Normal Distribution

Tossing a Coin

Properties of Exponents

Solve for x

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Sample Math Problems

Download FREE Math Resources

8 Math Hacks and Tricks to Turn Your 'Okay' Math Student Into a Math Champion!

How to Make Sure Your Child is Highly Successful and Becomes a Millionaire

Practice Math Problems