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

Answer:

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

Step-by-step 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

$x=\frac{-1+\sqrt{1^2-4\cdot \:1\left(-2\right)}}{2\cdot \:1}, \frac{-1-\sqrt{1^2-4\cdot \:1\left(-2\right)}}{2\cdot \:1}\\\Rightarrow x=1, -2$

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)