Three quadratic polynomials and three descriptions of parabolae are given below.
Polynomials:
P1(x)=2x2−8x+6P2(x)=−x2−2x+3P3(x)=x2+4x+7
Descriptions of graphs:
A. An upward–opening parabola that cuts the x–axis at two distinct positive points.
B. A downward–opening parabola that intersects the x–axis at one negative and one positive point.
C. An upward–opening parabola that does not intersect the x–axis at all.
a. (i) Match each polynomial to the correct description A, B or C.
b. (ii) For every match, justify your choice by referring to appropriate algebraic features of the polynomial.