which is the graph of $f(x)=(x - 1)(x + 4)$?
which is the graph of $f(x)=(x - 1)(x + 4)$?
Answer
Explanation:
Step1: Find the x - intercepts
Set (f(x)=(x - 1)(x + 4)=0). By the zero - product property, (x-1 = 0) gives (x = 1) and (x+4=0) gives (x=-4). So the x - intercepts are (x = 1) and (x=-4).
Step2: Determine the leading coefficient
Expand (f(x)=(x - 1)(x + 4)=x^{2}+4x-x - 4=x^{2}+3x - 4). The leading coefficient of the quadratic function (y=x^{2}+3x - 4) is (a = 1>0), so the parabola opens upward.
Answer:
The graph with x - intercepts at (x=-4) and (x = 1) and opening upward.