Question

Solve the following system of equations. Show all work and solutions. y = 2x2 + 6x + 4 y = −4x2 + 4

Answer 1

(0,4) (-1,0)

Explanation:

`y=2x^2 + 6x + 4`

`y = -4x^2 + 4`

Set the y equal to each other

`2x^2 + 6x + 4 = -4x^2 + 4`

Solve for x

`2x^2 + 6x + 4 = -4x^2 + 4\\6x^2+6x=0 \\6(x^2 + x) = 0\\x(x+1) = 0 \\x = 0, x = -1`

Solve for y

`y = -4(0)^2 + 4 \\=4\\y = -4(-1)^2 + 4 \\= 0`