f(x)=5x^2+3x+5 ; g(x) =7

Question

find points of intersection for the system of equations using algebra.

Answer 1

set f(x)=g(x)

5x^2+3x+5=7

5x^2+3x-2=0

factor if you can, otherwise complete the square or use the quadratic formula

(x+1)((5x-2)=0

x=--1 or 2/5

when x=-1 then f(x) =5(1)+3(-1)+5 = 10-3 = 7 = g(x) = 7

when x= 2/5 then f(x) = 5(2/5)^2 +3(2/5) + 5) = 4/5 + 6/5 + 5 = 2+5 = 7 = g(x) = 7