Question

use zeros to identify the graph of $f(x) = x^2 + x - 2$.

Explanation:

Step1: Find the zeros of the function

To find the zeros of \( f(x) = x^2 + x - 2 \), we set \( f(x) = 0 \), so we solve the quadratic equation \( x^2 + x - 2 = 0 \). We can factor this quadratic as \( (x + 2)(x - 1) = 0 \). Setting each factor equal to zero gives \( x + 2 = 0 \) or \( x - 1 = 0 \), so the zeros are \( x = -2 \) and \( x = 1 \).

Step2: Analyze the graphs based on zeros

We need to find the graph that intersects the x - axis at \( x=-2 \) and \( x = 1 \). Let's check each graph:

• For the first graph (top - left), we can see that it intersects the x - axis at \( x=-2 \) and \( x = 1 \).
• For the second graph (top - right), let's assume its x - intercepts are not \( -2 \) and \( 1 \) (by visual inspection, it seems to intersect at non - \( -2 \) and non - \( 1 \) points).
• For the third graph (bottom - left), its x - intercepts are not \( -2 \) and \( 1 \) (by visual inspection).
• For the fourth graph (bottom - right), its x - intercepts are not \( -2 \) and \( 1 \) (by visual inspection).

Answer:

The graph on the top - left (the first graph)