Find the x-intercepts for the parabola defined by this equation:
y=2x^2+ 4x - 6
Write your answer as two ordered pairs:
(x1.yı), (x2, y2)

(-3,0) (1,0)

Step-by-step explanation:

y=2x^2+ 4x - 6

Factor out the greatest common factor

y = 2( x^2 +2x -3)

Factor inside the parentheses

y = 2( x+3)(x-1)

Setting the equation equal to zero to find the x intercepts

0 =  2( x+3)(x-1)

Using the zero product property

x+3 = 0  x-1 =0

x = -3  x = 1

The x intercepts are

(-3,0) (1,0)

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form