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Approximate solutions from intersections of two graphs

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
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Question 1 of 8

Calculator allowed

Read the plotted rules as a graphical solution of the stated equation

The first rule is \(P(x)=x^{3} - 2x^{2}\). The second rule is \(Q(x)=-x\)

The graph shows the equation \(P(x)=Q(x)\) over x from -2 to 3 and y from -18 to 11. The horizontal grid interval is 1 unit; labelled ticks are 1 units apart

Cartesian graph of two rules over x from -2 to 3 and y from -18 to 11. The first curve is P(x)=x^3 -2x^2 and the second curve is Q(x)=-x. The curves are joined through exact rational plotted points on a one-unit horizontal grid.-2-10123-15-10-5510xy

Use only the intersections in the displayed window

(a)1 mark

Which equation represents the condition for an intersection?

(b)1 mark

How many intersection points are visible in the displayed window? Enter a whole number

Format: whole number
(c)2 marks

Record the intersection coordinates in increasing order of x. Use exact values for the horizontal coordinates

(d)1 mark

Which statement correctly describes the precision supported by the displayed graph?