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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The polynomial P is given exactly by the expression below. Let \(P(x)\) be given by:

P(x)=2(x-1)^{2}(x-2)^{2}

An exact calibration point is \(P(-\frac{3}{2})=\frac{1225}{8}\). Use the graph window \(-3\le x\le 3\) and \(-802\le y\le 1002\) for the graph selection

(a)5 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 vertical intercept \(P(0)\)

(b)1 mark

Select the description of the x-intercepts

At x=1, the graph touches the horizontal axis and turns. At x=2, the graph touches the horizontal axis and turns

At x=1, the graph crosses the horizontal axis with a stationary crossing. At x=2, the graph touches the horizontal axis and turns

At x=1, the graph crosses the horizontal axis without flattening. At x=2, the graph crosses the horizontal axis without flattening

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

Select the end behaviour of this polynomial

The graph falls on the left and rises on the right

The graph rises on the left and falls on the right

The graph rises on both the left and the right

The graph falls on both the left and the right

(d)1 mark

Choose the graph with the stated intercepts and end behaviour