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Approximate solutions from intersections of two graphs

Question 1 of 8

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

The first rule is \(P(x)=-\frac{1}{2}x^{3} - \frac{8}{3}x^{2} - \frac{8}{3}x + \frac{7}{3}\). The second rule is \(Q(x)=-x^{2} - 2x + 1\)

The graph shows the equation \(P(x)=Q(x)\) over x from -3 to 2 and y from -20 to 6. The horizontal grid interval is 1 unit; labelled ticks are 1 units apart

Use only the intersections in the displayed window

Use the graph to locate intersections and the displayed rules to check them. A grid position alone does not prove an exact value or a rounded value close to a rounding boundary

Keep the unrounded x-value, or sufficient guard digits, when finding its matching y-value. Round each requested coordinate separately only at the end

(a)1 mark

Which equation represents the condition for an intersection?

P(x)+Q(x)=0

P(x)-Q(x)=0

P(x)=0

Q(x)=0

(b)1 mark

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

Number of visible intersections Format: whole number

Record the visible intersection horizontal coordinates in increasing order. Give each x-coordinate to the nearest whole number

\(x_1\) (nearest whole number) \(x_2\) (nearest whole number)

(d)1 mark

Which reporting method matches the requested coordinate precision?

Every intersection has an exact integer x-coordinate, so no rounding or verification is needed

Report the requested nearest-whole-number coordinates. Check the equation if the plotted position is too close to a rounding boundary to decide

Only decimal approximations to two decimal places are required, irrespective of the stated answer precision