Question

One x-intercept for a parabola is at the point

(-5,0). Use the factor method to find the other
X-intercept for the parabola defined by this
equation:
y=x2 + 3x - 10
Separate the values with a comma.

Answer 1

(2, 0)

Explanation:

Given

y = x² + 3x - 10

To find the x- intercepts let y = 0, that is

x² + 3x - 10 = 0 ← in standard form

Consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)

The factors are + 5 and - 2, since

5 × - 2 = - 10 and 5 - 2 = + 3, hence

(x + 5)(x - 2) = 0

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 2 = 0 ⇒ x = 2

x- intercepts are (- 5, 0) and (2, 0)