we have
[tex]f(x)=x^{2} +2x-15[/tex]
we know that
The x-intercept is the value of x when the value of the function is equal to zero
so
in this problem
Find the roots of the function
equate the function to zero
[tex]x^{2} +2x-15=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2} +2x=15[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]x^{2} +2x+1=15+1[/tex]
[tex]x^{2} +2x+1=16[/tex]
Rewrite as perfect squares
[tex](x+1)^{2}=16[/tex]
Square root both sides
[tex](x+1)=(+/-)\sqrt{16}[/tex]
[tex](x+1)=(+/-)4[/tex]
[tex]x=-1(+/-)4[/tex]
[tex]x1=-1+4=3[/tex]
[tex]x2=-1-4=-5[/tex]
[tex]x^{2} +2x-15=(x-3)(x+5)[/tex]
therefore
the answer is
the x-intercepts are the points [tex](3,0)[/tex] and [tex](-5,0)[/tex]
