Hi, I am in a pre-calculus course and am having a problem with the following:

a) graph the equation

x2 - y - 4 = 0

x2 + y2 = 9
on the same set of coordinate axes.

I did not have a problem with this, I had a circle and a parabola with points (1,3) (-1,-3) (2,0) (-2,0) (3,5) and (-3,5).

The problem is part (b) of the question ask: Find all solutions of the system in part (a) algebraically. Express answers in decimal form, accurate to two decimal places.

I am having problems solving the math part.

y= x2 - 4 substitute into 2nd equation x2 + (x2 - 4)2 = 9

x2 + (x2 -4)(x2 - 4) = 9

x2 + x4 -8x2 - 16 = 9

x4 - 7x2 = 25

Now what? I know I need four answers as the circle cross my parabola at four points. Please help?

Thank you,

Hi Patty,

Ther are some errors in what you have done so far.

First (1,3) is not on the parabola, but (1,-3) is.

Also the line x2 + x4 -8x2 - 16 = 9 should read

x2 + x4 -8x2 + 16 = 9 and hence x4 - 7x2 + 7 = 0

This is a quadratic in x2, (x2)2 - 7x2 + 7 = 0. It doesn't factor but you can use the general quadratic to solve for x2. Since you are to give your answer is decimal form, convert the two values of x2 to decimal form and then take the square root to find x. This will give you 4 values for x.


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