Question

a submarine is moving inside the Atlantic ocean according to the formula y1=x2+2x-2. A school of fish is travelling inside the Atlantic ocean according to the formula of y2=- 0.5. scientists have approached you, in order to help them in the following:
1. On the same graph, draw the tracks of both the submarine and the school of fish.
2. Find the roots of the submarine track, by solving the y1 equation.
3. Identify the co-ordinates of intersection between the submarine and the school of fish.

Answer 1

Answer on Question #83642 – Math – Algebra

Question

A submarine is moving inside the Atlantic ocean according to the formula $y_1 = x_2 + 2x - 2$. A school of fish is travelling inside the Atlantic ocean according to the formula of $y_2 = -0.5$. Scientists have approached you, in order to help them in the following:

1. On the same graph, draw the tracks of both the submarine and the school of fish.

2. Find the roots of the submarine track, by solving the y1 equation.

3. Identify the co-ordinates of intersection between the submarine and the school of fish.

Solution

$$\begin{array}{l} 2. y_1 = x^2 + 2x - 2; \\ x^2 + 2x - 2 = 0; \\ D = 4 + 4 * 2 = 12; \\ x_1 = \frac{-2 - \sqrt{12}}{2} = -1 - \sqrt{3}; \\ x_2 = \frac{-2 + \sqrt{12}}{2} = -1 + \sqrt{3}; \\ \end{array}$$

$x_1, x_2$ are roots of the submarine track.

$$\begin{array}{l} 3. y_1 = x^2 + 2x + 1 - 3; \\ y_1 = (x + 1)^2 - 3; \\ y_2 = -0.5; \\ x^2 + 2x - 2 = -0.5; \\ x^2 + 2x - 1.5 = 0; \\ D = 4 + 4 * 1.5 = 10; \\ x_{11} = \frac{-2 - \sqrt{10}}{2} \approx -2.58; \\ x_{22} = \frac{-2 + \sqrt{10}}{2} \approx 0.52. \\ \end{array}$$

1.

Thus, $(-2.58; -0.5)$, $(0.52; -0.5)$ are coordinates of intersection between the submarine and the school of fish.

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