Question

brianna is graphing the function f(x) = x² + 6x + 5. what x-intercepts should brianna use to graph f(x)? -5 and -1 -5 and 1 -1 and 5 1 and 5

Explanation:

Step1: Find x-intercepts (set f(x)=0)

To find the x - intercepts of the function \( f(x)=x^{2}+6x + 5 \), we set \( f(x) = 0 \). So we have the quadratic equation \( x^{2}+6x + 5=0 \).

Step2: Factor the quadratic equation

We factor the quadratic expression \( x^{2}+6x + 5 \). We need two numbers that multiply to \( 5 \) and add up to \( 6 \). The numbers are \( 5 \) and \( 1 \). So, \( x^{2}+6x + 5=(x + 5)(x+1)=0 \).

Step3: Solve for x

Using the zero - product property, if \( (x + 5)(x + 1)=0 \), then either \( x+5 = 0 \) or \( x + 1=0 \).

• If \( x+5=0 \), then \( x=-5 \).
• If \( x + 1=0 \), then \( x=-1 \).

Answer:

-5 and -1 (corresponding to the first option: \(\boldsymbol{-5}\) and \(\boldsymbol{-1}\))