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dem82 [27]
3 years ago
8

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 yo

ur result both algebraically and graphically.

Mathematics
1 answer:
ycow [4]3 years ago
5 0

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)

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