Solving quadratic inequalities algebraically | Maths | Quizalize & Oak National Academy

Starter quiz

$(x+8)(x-2)$ is the quadratic $x^2+6x-16$ in __________ form.

factorised ✓

solution

expression

equation

inequality
Match the quadratics to their factorised form.

$x^2+15x+54$

⇔

$(x+9)(x+6)$ ✓

$x^2+3x-54$

⇔

$(x+9)(x-6)$ ✓

$x^2-3x-54$

⇔

$(x-9)(x+6)$ ✓

$x^2-15x+54$

⇔

$(x-9)(x-6)$ ✓

$2x^2+24x+54$

⇔

$(x+9)(2x+6)$ ✓

$2x^2+21x+54$

⇔

$(2x+9)(x+6)$ ✓
If $x^2-7x-30=0$ factorises to $(x-10)(x+3)=0$ , where are its roots?

$x=10$ ✓

$x=-10$

$x=3$

$x=-3$ ✓

$x=-30$
Which of the below is the quadratic formula?

$x={{-b\pm{\sqrt{b^2-4ac}}}\over{2a}}$ ✓

$x={{b\pm{\sqrt{b^2-4ac}}}\over{2a}}$

$x=-b\pm{{\sqrt{b^2-4ac}}\over{2a}}$

$x=-b+{{\sqrt{b^2-4ac}}\over{2a}}$

$x={{-b+{\sqrt{b^2-4ac}}}\over{2a}}$
This is a sketch of $y=x^2-10x+24$ . Use it to solve this inequality: $x^2-10x+24<0$ .

$x<6$

$4 ✓$

$10$

$x<4$ or $x>6$

$x>4$ or $x>6$
Which of these is a rearrangement of $x^2-10x-87=0$ when completing the square?

$(x-5)^2=87$

$(x-5)^2=-87$

$(x-5)^2=62$

$(x-5)^2=-112$

$(x-5)^2=112$ ✓

Exit quiz

The curve $y=x^2+2x-15$ has __________ at $x=-5$ and $x=3$ .

solutions

equations

roots ✓

turning points
Solve $x^2+2x-15<0$ .

$x<3$

$x<-5$

$-5 ✓$

$x<-5$ and $x>3$

There is no solution to this inequality.
Solve $x^2+2x-15>0$ .

$x>0$

$x<-5$ or $x>3$ ✓

$-5$

$x<-5$ or $x<3$

There is no solution to this inequality.
Solve $x^2-9<16$ .

$-5 ✓$

$x<-5$ and $x>5$

$-3$

$x<-3$ and $x>3$

There is no solution to this inequality.
Solve $-x^2-2x+15>0$ .

$x<-5$ and $x>3$

$x<-3$ and $x>5$

$x>-5$ and $x>3$

$-5 ✓$

$-3$
The solution to $2x^2-5x+20 is 3$ ______.

'10' ✓

Worksheet

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Lesson Details

Key learning points

The solutions to the quadratic equation can be found using one of your known methods
By sketching the graph, it is easy to define the solution set
By studying the features of the quadratic, it is easy to define the solution set

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