Sketch both the circle $x^{2} + y^{2} = 25$ and the parabola $y = x^{2} − 13$.

1. How many points of intersection are there?

   Hint (a):

   Look at the graph at right.

   Answer (a):

   $4$ points

2. Find the coordinates of these points algebraically.

   Step 1(b):

   Substitute $x^{2} − 13$ into the first equation.
   
   x^{$^{2} + \left(x^{2} − 13\right)^{2} = 25$}

   Step 2(b):

   Solve for $x$.
   
   $x^{4} − 25x^{2} + 144 = 0$

   Step 3(b):

   Factor the equation.
   
   $\left(x^{2} − 16\right)\left(x^{2} − 9\right)$

   Step 4(b):

   $\left(x − 4\right)\left(x + 4\right)\left(x − 3\right)\left(x + 3\right)$

   Partial Answer (b):

   $x = ±4, ±3$

   Step 5(b):

   Now substitute in these $x$ values to find the $y.$