Consider the function .

MATHEMATICS · Multi-part · AoPS · Mathematics · Quadratic Equations - Part 1 · Quadratic Equations - Part 1

Problem

Consider the function

s(x)=-(x-2)^{2}+3

. (i) Expand

s(x)

and write it in standard polynomial form

a_2x^{2}+a_1x+a_0

. (ii) State the degree of

s(x)

and classify it. (iii) Determine the leading coefficient of

s(x)

and state whether the graph opens upwards or downwards, giving a reason based on the sign of the leading coefficient.