Two quadratic polynomials are given below: (g(x)=x^ 2 -6x+9 ) and (h(x)=2x^ 2 +3x-7 ).
MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Two quadratic polynomials are given below:
g(x)=x2−6x+9 and h(x)=2x2+3x−7.
(a) Without solving the equations, determine which of the two graphs y=g(x) or y=h(x) has more distinct x-intercepts. Justify your answer.
(b) For the polynomial that has the fewer number of x-intercepts, find its x-intercept(s), if any.
(c) Explain briefly how the sign and magnitude of the leading coefficient affect the shape of the parabola, even though they do not change the number of x-intercepts found in part (i).