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)

Answer 1

X^2 + 2x - 15 = 0
(x - 3)(x + 5) = 0
x = 3 or x = -5
left-most x-intercept: (-5, 0)
right-most x-intercept: (3, 0)

Answer 2

we have

$f(x)=x^{2} +2x-15$

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

$x^{2} +2x-15=0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^{2} +2x=15$

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2} +2x+1=15+1$

$x^{2} +2x+1=16$

Rewrite as perfect squares

$(x+1)^{2}=16$

Square root both sides

$(x+1)=(+/-)\sqrt{16}$

$(x+1)=(+/-)4$

$x=-1(+/-)4$

$x1=-1+4=3$

$x2=-1-4=-5$

$x^{2} +2x-15=(x-3)(x+5)$

therefore

the answer is

the x-intercepts are the points $(3,0)$ and $(-5,0)$