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).