SOLUTION: How would I solve this problem? Graph the equations of the system. Then solve the system to find the points of intersection. y = x to the power of 2 - 6x + 9 y = -x + 3 D

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How would I solve this problem? Graph the equations of the system. Then solve the system to find the points of intersection. y = x to the power of 2 - 6x + 9 y = -x + 3 D      Log On


   

Question 436896: How would I solve this problem?
Graph the equations of the system. Then solve the system to find the points of intersection.
y = x to the power of 2 - 6x + 9
y = -x + 3
Do I need to find the intersections first before I can graph?
Thank you very much for your help.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+x%5E2+-+6x+%2B+9
y+=+-x+%2B+3
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+-+6x+%2B+9%2C+-x+%2B+3%29+

as you can see from the graph, intersections are at :
(2,1) and (3,0)
let's check it:
y+=+x%5E2+-+6x+%2B+9...substitute y with -x+%2B+3
-x+%2B+3+=+x%5E2+-+6x+%2B+9
+x%5E2+-+6x+%2Bx+-+3+%2B+9=0
+x%5E2+-+5x+%2B+6=0.use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-5%29+%2B-+sqrt%28%28-5%29%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29+
x+=+%285+%2B-+sqrt%2825-24+%29%29%2F2+
x+=+%285+%2B-+sqrt%281%29%29%2F2+
x+=+%285+%2B-+1%29%29%2F2+
x+=+%285+%2B1%29%2F2+
x+=+6%2F2+
x+=+3+.......one solution

x+=+%285+-1%29%2F2+
x+=+4%2F2+
x+=+2+.......another solution
now find y
y+=+-x+%2B+3.......if x+=+3+
y+=+-3+%2B+3
y+=+0
y+=+-x+%2B+3.......if x+=+2+
y+=+-2+%2B+3
y+=1
so, you get points (3,0) and (2,1) as seen on a graph