Question

find the x-intercepts of the function. enter each solution as an ordered pair. write values as fractions or decimals rounded to two places if necessary. f(x) = x² + 15x + 50 show your work here

Explanation:

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

To find the \( x \)-intercepts, we set \( f(x)=0 \), so we have the equation \( x^{2}+15x + 50=0 \).

Step2: Factor the quadratic equation

We need to factor \( x^{2}+15x + 50 \). We look for two numbers that multiply to \( 50 \) and add up to \( 15 \). The numbers \( 5 \) and \( 10 \) work because \( 5\times10 = 50 \) and \( 5 + 10=15 \). So we can factor the quadratic as \( (x + 5)(x+ 10)=0 \).

Step3: Solve for \( x \)

Using the zero - product property, if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \). So we set each factor equal to zero:

• For \( x + 5=0 \), we subtract \( 5 \) from both sides of the equation: \( x=-5 \).
• For \( x + 10=0 \), we subtract \( 10 \) from both sides of the equation: \( x=-10 \).

Answer:

The \( x \)-intercepts are \( (-5,0) \) and \( (-10,0) \)