Question

Graph the line given by x+y=-2 and the quadratic curve given by y=x²-4. Find all solutions to the system of equations. Verify your result both algebraically and graphically.

Answer 1

(1,-3) and (-2,0)

Explanation:

`x+y=-2`

`y=x^2-4`

Applying the second equation to the first

`x+x^2-4=-2\\\Rightarrow x+x^2-4+2=0\\\Rightarrow x^2+x-2=0`

Solving the equation we get

`x=(-1+√(1^2-4\cdot \:1\left(-2\right)))/(2\cdot \:1), (-1-√(1^2-4\cdot \:1\left(-2\right)))/(2\cdot \:1)\\\Rightarrow x=1, -2`

When x = 1

`y=-2-1\\\Rightarrow y=-3`

When x = -2

`y=-2-(-2)\\\Rightarrow y=0`

So, the line and curve will intersect at points (1,-3) and (-2,0)