# What graph correctly solves the system of equations below?

# y = −x^{2} − 1; y = 2x^{2} − 4.

Quadratic equations are equations with degrees equal to two. They can have at most two roots. A system of two quadratic equations can have at most two solutions, that is, the points where they intersect.

### Answer: The solution to the system of equations given y = −x^{2} − 1; y = 2x^{2} − 4, is (-1, -2) and (1, -2).

Let's understand the solution in detail.

**Explanation:**

Given system of equations:

⇒ y = −x^{2} − 1

⇒ y = 2x^{2} − 4

Now, we equate both the equations given since both of them are equal to y.

⇒ −x^{2} − 1 = 2x^{2} − 4

⇒ 3x^{2} - 3 = 0

Solving the above equation for x, we get:

⇒ x = 1 or x = -1

Now, we find the corresponding values of y, using either of the equations: y = -(-1)^{2} - 1 = -2 or y = -(1)^{2} - 1 = -2

We get the solutions (-1, -2) and (1, -2).

Now, we plot the system of equations in the graph as shown below.

From the graph, we can clearly see that both the curves intersect at the point (-1, -2) and (1, -2) which are the solutions to the system of equations given.