Find where two parabolas intersect

Question

needs to use substitution 

 

Y= X^2+5 & y= x^2 + 2x+1

 

Algebra 1


need to show work

Answer 1

y= x² + 5

y= x² + 2x + 1

 

This translates into:

x² + 5 = x² + 2x + 1

because we're substituting the equations for y.

 

We start by subtracting the squares:

5 = 2x + 1

 

From here, it's just isolating x:

4 = 2x

2 = x

So the two parabolas intersect at x = 2, not we need to find the value of y to get the other part of our point set:

y = 2² + 5

y = 4 + 5

y = 9

 

Check:

y = 2² + 2 * 2 + 1

y = 4 + 4 + 1

y = 9

 

So the two parabolas intersect at (2, 9)