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Year 11
Higher

Solving quadratic inequalities in one variable graphically

I can solve a quadratic inequality graphically.

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New
New
Year 11
Higher

Solving quadratic inequalities in one variable graphically

I can solve a quadratic inequality graphically.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. A quadratic equation can be represented graphically
  2. The solutions are where the graph cross the x axis
  3. By studying the graph, you can see where the equation is greater than 0
  4. By studying the graph, you can see where the equation is less than 0
  5. The solution set can be represented algebraically or using set notation

Keywords

  • Inequality - An inequality is used to show that one expression may not be equal to another.

  • Quadratic - A quadratic is an equation, graph or sequence where the highest exponent of the variable is 2. The general form for a quadratic is ax^2 + bx + c

Common misconception

All inequalities are graphed with solid lines.

When graphed, strict inequalities are indicated with a dashed line. This is important as it visually tells us that values on the line will not satisfy the inequality.

Encourage pupils to identify the region that satisfies multiple inequalities in different ways: graphically, testing a point, algebraically.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
When graphed, a quadratic equation forms...
an upward curve.
a straight line.
a wave.
Correct answer: a parabola.
Q2.
Solve $$x^2-64=0$$.
$$x=64$$
$$x=8$$
$$x=-8$$
Correct answer: $$x=8$$ and $$x=-8$$
The equation has no solutions.
Q3.
Find the roots of $$x^2-3x-10=0$$.
$$x=3$$
$$x=-10$$
Correct answer: $$x=5$$
$$x=-5$$
Correct answer: $$x=-2$$
Q4.
This could be the sketch of which one of these quadratics?
An image in a quiz
Correct answer: $$x^2-10x+21$$
$$x^2-4x-21$$
$$x^2+4x-21$$
$$x^2+10x+21$$
$$-x^2+10x-21$$
Q5.
What is the minimum value of this quadratic?
An image in a quiz
Correct answer: $$-4$$
$$3$$
$$7$$
$$0$$
$$-3$$
Q6.
The solution to $$2x^2-14=x^2-3x+14$$ is $$x=4$$ and $$x=$$ .
Correct Answer: -7, x=-7

Exit quiz

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6 Questions

Q1.
$$-5<x<5$$ is the __________ the quadratic inequality $$x^2-25<0$$.
Correct answer: solution to
graph of
inequality of
root of
Q2.
This is the curve $$y=x^2-9$$ Use the graph to solve $$x^2-9<0$$.
An image in a quiz
$$x<3$$
Correct answer: $$-3<x<3$$
$$x<-3$$ or $$x>3$$
$$x=-3$$ or $$x=3$$
This inequality has no solutions.
Q3.
This is the curve $$y=x^2-9$$. Use the graph to solve $$x^2-9>0$$.
An image in a quiz
$$x>3$$
$$-3<x<3$$
Correct answer: $$x<-3$$ or $$x>3$$
$$x>-3$$ or $$x<3$$
The inequality has no solutions.
Q4.
This is the curve $$y=x^2-9$$. Use the graph to solve $$x^2-9<-9$$.
An image in a quiz
$$x=0$$
$$y<-9$$
$$x<0$$
$$x<-3$$ or $$x>3$$
Correct answer: The inequality has no solutions.
Q5.
This is the curve $$y=x^2-4x+4$$. The solution to the inequality $$1<x^2-4x+4<4$$ is $$0<x<1$$ or .
An image in a quiz
Correct Answer: 3<x<4, 3 < x < 4
Q6.
Rearrange and sketch to solve $$100-x^2<64$$.
$$x<-8$$ or $$x>8$$
Correct answer: $$x<-6$$ or $$x>6$$
$$-6<x<6$$
$$-8<x<8$$
$$-10<x<10$$