Inequalities

Hong Kong

Stage 4 - Stage 5

We want to find the x-values that satisfy the inequality$\left(x-3\right)\left(x-2\right)<0$(`x`−3)(`x`−2)<0.

a

Find the $x$`x`-values of the $x$`x`-intercepts of the curve described by $y=\left(x-3\right)\left(x-2\right)$`y`=(`x`−3)(`x`−2).

Write both answers on the same line separated by commas.

b

Find the $y$`y`-value of the $y$`y`-intercept of the curve.

c

Hence plot the curve for $y=\left(x-3\right)\left(x-2\right)$`y`=(`x`−3)(`x`−2).

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d

Hence solve the inequality $\left(x-3\right)\left(x-2\right)<0$(`x`−3)(`x`−2)<0.

Easy

Approx 7 minutes

We want to solve $x^2-x-2>0$`x`2−`x`−2>0 by plotting the associated parabola $y=x^2-x-2$`y`=`x`2−`x`−2.

We want to solve $-x^2+2x+3\le0$−`x`2+2`x`+3≤0 by first plotting the associated parabola $y=-x^2+2x+3$`y`=−`x`2+2`x`+3.

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