Which one is it in the screenshot below?
2 answers:
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Answer: (-2, 0) and (0, -2)
Step-by-step explanation:
This system is:
y + x = -2
y = (x + 1)^2 - 3
To solve this we first need to isolate one of the variables in one fo the equations, in the second equation we have already isolated the variable y, so we can just replace it in the first equation:
(x + 1)^2 - 3 + x = -2
Now we can solve this for x.
x^2 + 2*x + 1 - 3 = -2
x^2 + 2*x + 1 -3 + 2 = 0
x^2 + 2*x + 0 = 0
The solutions of this equation are given by the Bhaskara's formula, then the solutions are:
The two solutions are:
x = (-2 - 2)/2 = -2
In this case, we replace this value of x in the first equation and get:
y - 2 = -2
y = -2 + 2 = 4
This solution is x = -2, y = 0, or (-2, 0)
The other solution for x is:
x = (-2 + 2)/2 = 0
If we replace this in the first equation we get:
y + 0 = -2
y = -2
This solution is x = 0, y = -2, or (0, -2)
Answer:
Step-by-step explanation:
Standard form of a parabola with a vertical axis of symmetry:
If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.
From inspection of the graph:
- Vertex = (3, -1)
- Directrix = y = -3
Therefore:
- h = 3
- k = -1
- k - p = -3
Use the Directrix equation to find p
⇒ y = (k - p)
⇒ -3 = -1 - p
⇒ p = 2
Therefore the equation of the conic section is:
Rearranging in standard form :