Question

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

Answer 1

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Solve for the first variable in one of the equations, then substitute the result into the other equation.Point Form:

(√102,−32),(−√102,−32)

Equation Form:

x=√10/2,y = −3/2

x=−√10/2,y = −3/2

Answer 2

The equations are

y = -
`x^(2)` - 1

y = 2
`x^(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 =2
`x^(2)` - 4

3
`x^(2)` -3 =0

3(
`x^(2)` -1) = 0

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

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

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