Question

which function has zeros of - 4 and 2?
a. $f(x) = x^2 + 7x - 8$
b. $g(x) = x^2 - 7x - 8$
c. image of a parabola
d. image of a parabola
teacher feedback/next steps for practice
recall definition of zeros/roots/x-intercepts
identify zeros from graphs and tables and write as a value

Explanation:

Step1: Recall zero-factor property

If a function has zeros at \( x = -4 \) and \( x = 2 \), then the factored form is \( f(x)=(x + 4)(x - 2) \).

Step2: Expand the factored form

Expand \( (x + 4)(x - 2) \):
\( x(x - 2)+4(x - 2)=x^{2}-2x + 4x - 8=x^{2}+2x - 8 \). Wait, maybe check the graphs. For a parabola with zeros at -4 and 2, the x - intercepts are at \( x=-4 \) (left of y - axis) and \( x = 2 \) (right of y - axis). Let's check the graphs:

• Graph c: Let's see the x - intercepts. From the grid, the left x - intercept seems to be at \( x=-4 \) (since it's 4 units left of y - axis) and right at \( x = 2 \) (2 units right of y - axis).
• Graph d: The x - intercepts look more centered, maybe around -1 and 3? Not -4 and 2. Now check the equations:

For option a: \( f(x)=x^{2}+7x - 8 \). Factor: \( (x + 8)(x - 1) \), zeros at -8 and 1. Not -4 and 2.
For option b: \( g(x)=x^{2}-7x - 8=(x - 8)(x + 1) \), zeros at 8 and -1. Not -4 and 2. So the graph with zeros at -4 and 2 is graph c.

Answer:

c (the graph labeled c with x - intercepts at -4 and 2)