Question

consider the function f(x) = x² + 2x - 15. what are the x-intercepts of the function? left-most x-intercept: ( , 0) right-most x-intercept: ( , 0)

Explanation:

Step1: Set \( f(x) = 0 \)

To find the \( x \)-intercepts, we set \( f(x)=0 \), so we have the equation \( x^{2}+2x - 15=0 \).

Step2: Factor the quadratic equation

We factor the quadratic expression \( x^{2}+2x - 15 \). We need two numbers that multiply to \( - 15 \) and add up to \( 2 \). The numbers are \( 5 \) and \( - 3 \), so we can factor the equation as \( (x + 5)(x - 3)=0 \).

Step3: Solve for \( x \)

Using the zero - product property, if \( (x + 5)(x - 3)=0 \), then either \( x+5 = 0 \) or \( x - 3=0 \).

• For \( x+5 = 0 \), we subtract \( 5 \) from both sides of the equation and get \( x=-5 \).
• For \( x - 3=0 \), we add \( 3 \) to both sides of the equation and get \( x = 3 \).

Answer:

Left - most \( x \)-intercept: \( (-5,0) \)
Right - most \( x \)-intercept: \( (3,0) \)