Connect a factorised higher-degree rule and its graph practice questions | Mathematical Methods (Year 11, VCE Units 1 & 2, Higher-degree polynomials, Power functions and factorised forms)

Question 1 of 8

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Use the polynomial data shown below. Let \(P(x)\) be given by:

P(x)=-2(x-\frac{2}{3})^{2}(x+\frac{1}{2})(x+2)

An exact calibration point is \(P(0)=-\frac{8}{9}\). Use the graph window \(-3\le x\le 3\) and \(-411\le y\le 193\) for the graph selection

(a)7 marks

Use the stated factorised rule to complete the table of ordered x-intercepts, their multiplicities and the vertical intercept

\(x\)-intercept 1 in increasing order multiplicity at \(x\)-intercept 1 \(x\)-intercept 2 in increasing order multiplicity at \(x\)-intercept 2 \(x\)-intercept 3 in increasing order multiplicity at \(x\)-intercept 3 vertical intercept \(P(0)\)

(b)1 mark

Which intercept description is consistent with P?

At x=-2, the graph touches the horizontal axis and turns. At x=-1/2, the graph crosses the horizontal axis without flattening. At x=2/3, the graph touches the horizontal axis and turns

At x=-2, the graph crosses the horizontal axis without flattening. At x=-1/2, the graph crosses the horizontal axis without flattening. At x=2/3, the graph touches the horizontal axis and turns

At x=-2, the graph crosses the horizontal axis with a stationary crossing. At x=-1/2, the graph crosses the horizontal axis without flattening. At x=2/3, the graph touches the horizontal axis and turns

At x=-2, the graph touches the horizontal axis and turns. At x=-1/2, the graph touches the horizontal axis and turns. At x=2/3, the graph crosses the horizontal axis without flattening

Which statement gives both end directions?

The graph rises on the left and falls on the right

The graph falls on the left and rises on the right

The graph falls on both the left and the right

The graph rises on both the left and the right

(d)1 mark

Which graph represents this polynomial?