Consider the following four polynomials:

MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials

Problem

Consider the following four polynomials: A(x)=x2−5x+6A(x)=x^{2}-5x+6 B(x)=−2x2+4x+6B(x)=-2x^{2}+4x+6 C(x)=x2+3C(x)=x^{2}+3 D(x)=−3x+4D(x)=-3x+4 (i) Sketch rough graphs of y=A(x),  B(x),  C(x)y=A(x),\;B(x),\;C(x) and y=D(x)y=D(x) on the same set of axes, clearly showing intercepts on both axes. (ii) From your sketches, list the polynomials whose graphs never meet the xx–axis. (iii) Identify any pair of polynomials whose graphs share the same yy–intercept, giving reasons based on their equations. (iv) Among the four graphs, name those that represent curves opening downwards or lines with negative slope, with justification from the coefficients.

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