Question

use the graph of the function to write the equation in factored form.
write the equation

Explanation:

Step1: Identify x-intercepts

The graph intersects the x-axis at \( x = -6 \) and \( x = -1 \), so the factors are \( (x + 6) \) and \( (x + 1) \). Let the function be \( y = a(x + 6)(x + 1) \).

Step2: Find the value of \( a \)

Use the y-intercept \( (0, 6) \). Substitute \( x = 0 \), \( y = 6 \) into the equation:
\( 6 = a(0 + 6)(0 + 1) \)
\( 6 = 6a \)
Divide both sides by 6: \( a = 1 \).

Step3: Write the factored form

Substitute \( a = 1 \) into \( y = a(x + 6)(x + 1) \), so the equation is \( y = (x + 6)(x + 1) \).

Answer:

\( y = (x + 6)(x + 1) \)