Question

Which graph correctly solves the system of equations below? y = −x2 − 1 y = 2x2 − 4 (6 points)

Answer 1

Well, it's parabola and the vertex is (0,4) the Axis of symmetry is 0 and the Directrix is y= 49/12

Answer 2

The equations are


`i) y=-x^2-1\\\\ii) y=2x^2-4`,

The graphs of the solutions (x, y) of these equations are 2 parabolas, since the right hand side expressions are polynomials of degree 2.


The solution/s of the system are the x-coordinates of the point/s of intersection of the parabolas.


The solutions of the first equation form a parabola looking downwards (since the coefficient of x^2 is -), and the second, a parabola opening upwards (since the coefficient of x^2 is +).

We can draw both parabolas, but to find the solution we still need to solve the system algebraically.

The algebraic solution of the system is:


`-x^2-1=2x^2-4\\\\3x^2-3=0\\\\3(x^2-1)=0\\\\x^2-1=0`, so

the solutions are x=-1 and x=1.

The graph of the system is drawn using desmos.com


If we are allowed to use a graphic calculator, we can draw both graphs and point at the solution.