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Approximate solutions from intersections of two graphs

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
power-and-line, degree 2, multiplicities 1,1, exact-grid, horizontal coordinatespower-and-line, degree 2, multiplicities 1,1, graph-supported, horizontal coordinatespolynomial-and-line, degree 2, multiplicities 1,1, exact-grid, horizontal coordinatespolynomial-and-line, degree 2, multiplicities 1,1, graph-supported, horizontal coordinatespolynomial-and-lower-degree-polynomial, degree 2, multiplicities 1,1, exact-grid, horizontal coordinatespolynomial-and-lower-degree-polynomial, degree 2, multiplicities 1,1, graph-supported, horizontal coordinatesNOWMix of allRecommended
Question 1 of 8

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Analyse where the two displayed rules have equal outputs

The first rule is \(P(x)=-2x^{2} - 5x + 1\). The second rule is \(Q(x)=-x + 1\)

The graph shows the equation \(P(x)=Q(x)\) over x from -4 to 2 and y from -19 to 7. The horizontal grid interval is 1 unit; labelled ticks are 1 units apart

Cartesian graph of two rules over x from -4 to 2 and y from -19 to 7. The first curve is P(x)=-2x^2 -5x +1 and the second curve is Q(x)=-x +1. The curves are joined through exact rational plotted points on a one-unit horizontal grid.-4-3-2-1012-15-10-55xy

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

(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 reporting method matches the requested coordinate precision?