Question

Find the other x-intercept for the parabola defined by this equation y=2x2+3-2​

Answer 1

(
`(1)/(2)`, 0 )

Explanation:

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

2x² + 3x - 2 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 2 = - 4 and sum = + 3

The factors are + 4 and - 1

Use these factors to split the x- term

2x² + 4x - x - 2 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) - 1 (x + 2) ← factor out (x + 2) from each term

(x + 2)(2x - 1) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

2x - 1 = 0 ⇒ 2x = 1 ⇒ x =
`(1)/(2)`

The x- intercepts are (- 2, 0 ), (
`(1)/(2)`, 0 )