Solving quadratic inequalities in one variable graphically | Maths

Starter quiz

When graphed, a quadratic equation forms...

an upward curve.

a straight line.

a wave.

a parabola. ✓
Solve $x^2-64=0$ .

$x=64$

$x=8$

$x=-8$

$x=8$ and $x=-8$ ✓

The equation has no solutions.
Find the roots of $x^2-3x-10=0$ .

$x=3$

$x=-10$

$x=5$ ✓

$x=-5$

$x=-2$ ✓
This could be the sketch of which one of these quadratics?

$x^2-10x+21$ ✓

$x^2-4x-21$

$x^2+4x-21$

$x^2+10x+21$

$-x^2+10x-21$
What is the minimum value of this quadratic?

$-4$ ✓

$3$

$7$

$0$

$-3$
The solution to $2x^2-14=x^2-3x+14$ is $x=4$ and $x=$ ______.

'-7' ✓

Exit quiz

$-5 is the __________ the quadratic inequality x^2-25<0 .$

solution to ✓

graph of

inequality of

root of
This is the curve $y=x^2-9$ Use the graph to solve $x^2-9<0$ .

$x<3$

$-3 ✓$

$x<-3$ or $x>3$

$x=-3$ or $x=3$

This inequality has no solutions.
This is the curve $y=x^2-9$ . Use the graph to solve $x^2-9>0$ .

$x>3$

$-3$

$x<-3$ or $x>3$ ✓

$x>-3$ or $x<3$

The inequality has no solutions.
This is the curve $y=x^2-9$ . Use the graph to solve $x^2-9<-9$ .

$x=0$

$y<-9$

$x<0$

$x<-3$ or $x>3$

The inequality has no solutions. ✓
This is the curve $y=x^2-4x+4$ . The solution to the inequality $1 is 0 or$ ______.

'3<x<4' ✓
Rearrange and sketch to solve $100-x^2<64$ .

$x<-8$ or $x>8$

$x<-6$ or $x>6$ ✓

$-6$

$-8$

$-10$

Worksheet

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Lesson Details

Key learning points

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

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.

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