Question

onsider 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

To find the x-intercepts of the function \( f(x) = x^2 + 2x - 15 \), we set the function equal to zero and solve for \( x \):

\[
x^2 + 2x - 15 = 0
\]

Now, we can factor the quadratic equation. We want two numbers that multiply to \(-15\) (the constant term) and add to \(2\) (the coefficient of the linear term). The numbers \(5\) and \(-3\) satisfy these conditions because \(5 \cdot (-3) = -15\) and \(5 + (-3) = 2\).

So, we can factor the quadratic as follows:

\[
(x + 5)(x - 3) = 0
\]

Next, we set each factor equal to zero to find the x-intercepts:

1. \(x + 5 = 0\) leads to:
\[
x = -5
\]

2. \(x - 3 = 0\) leads to:
\[
x = 3
\]

Thus, the x-intercepts are at the points:

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

In conclusion:

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

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