SOLUTION: Solve the system and graph the curves: a) x^2+3x-y+2 = 0 ; and y-5x = 1

Algebra ->  Systems-of-equations -> SOLUTION: Solve the system and graph the curves: a) x^2+3x-y+2 = 0 ; and y-5x = 1      Log On


   

Question 1048624: Solve the system and graph the curves:
a) x^2+3x-y+2 = 0 ; and y-5x = 1
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
SOLVING

x%5E2%2B3x-%285x%2B1%29%2B2=0
x%5E2%2B3x-5x-1%2B2=0
x%5E2-2x%2B1=0
%28x-1%29%5E2=0
intersecting coordinate x=1.
Corresponding vertical coordinate, y=5x%2B1=5%2A1%2B1=6, for the single point (1,6).



GRAPHING

The line is straightforward.

the parabola can be converted into standard form for easy finding of roots and vertex. OR, factoring could help, if possible.

y=x%5E2%2B3x%2B2
y=%28x%2B1%29%28x%2B2%29
Roots being -1 and -2, symmetric around x=-3%2F2;
y for the vertex, .
-
Vertex is at (-3/2, -1/4).



graph%28400%2C400%2C-3%2C7%2C-3%2C7%2Cx%5E2%2B3x%2B2%2C5x%2B1%29

A closer look at the intersection:
graph%28400%2C400%2C-1%2C3%2C2%2C7%2Cx%5E2%2B3x%2B2%2C5x%2B1%29

Answer by ikleyn(52858) About Me  (Show Source):
You can put this solution on YOUR website!
.
Intersecting is touching at x = 1 in this case.