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

Find the other x-intercept for the parabola defined by this equation y=2x2+3-2​-example-1
User Gonkers
by
8.5k points

1 Answer

5 votes

Answer:

(
(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 )

User JeffD
by
8.3k points

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