determine the solution(s) to the following equations using your graphing calculator f(x) = x2+2x-8 g(x) = 2x+1

Question

determine the solution(s) to the following equations using your graphing calculator

f(x) = x²+2x-8

g(x) = 2x+1

Answer 1

(3, 7) and (-3,-5) are the two points where the graphs intersect

f(x) is upward opening parabola which below the line from x=-3 to x=3

g(x) is a straight line with slope = +2

f(x)=g(x) when they intersect

x^2 +2x-8 = 2x +1

subtract 2x from both sides

x^2 -8 =1

add 8 to both sides

x^2 =1+8=9

x = + or- sqr9

x = 3 or -3

y = 2(3)+1 =7

y= (-3)^2 +2(-3)-8 = 9-6-8 = -5

points of intersection are (3,7) and (-3,-5)

the parabola has vertex (-1,-9) and x intercepts -4 and 2, y intercept -8

the line has y intercept 1