Question

question 8 of 10
which graph is defined by the function given below?
y = (x - 1)(x + 4)
four graphs labeled a, b, c, d
click here for long description
a. graph a
b. graph b
c. graph c
d. graph d

Explanation:

Step1: Find x-intercepts

Set \( y = 0 \), so \( (x - 1)(x + 4)=0 \). Then \( x - 1 = 0 \) or \( x + 4 = 0 \), giving \( x = 1 \) and \( x = - 4 \). The graph should cross the x - axis at \( x=-4 \) and \( x = 1 \).

Step2: Analyze the parabola's direction

The function is a quadratic in the form \( y=(x - 1)(x + 4)=x^{2}+3x - 4 \). The coefficient of \( x^{2} \) is \( 1>0 \), so the parabola opens upwards.

Step3: Match with graphs

Looking at the options, Graph A has x - intercepts around \( x=-4 \) and \( x = 1 \) (or positions consistent with these roots) and opens upwards. Graphs B, C, D have x - intercepts not matching \( x=-4 \) and \( x = 1 \) (B seems to have a root near 0, C and D are symmetric about y - axis which would imply roots at \( x = a \) and \( x=-a \), not \( - 4 \) and \( 1 \)).

Answer:

A. Graph A