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Home > A2C > Chapter 9 > Lesson 9.3.2 > Problem 9-152

9-152.
  1. Sketch both the circle x2 + y2 = 25 and the parabola y = x2 − 13. Homework Help ✎

    1. How many points of intersection are there?

    2. Find the coordinates of these points algebraically.

Look at the graph at right.

4 points

Substitute x2 − 13 into the first equation.

x2 + (x2 − 13)2 = 25

Solve for x.

x4 − 25x2 + 144 = 0

Factor the equation.

(x2 − 16)(x2 − 9)

(x − 4)(x + 4)(x − 3)(x + 3)

x = ±4, ±3

Now substitute in these x values to find the y.