Points of Intersection

Question

Given that f(x)=1/7x^2-2x+3 and g(x)=-1/2x+2, use the graphing feature of a TI-89 calculator to find the points of intersection, rounded to 3 decimal places.

Answer 1

Here is the graph on Desmos that found the points of intersection too:

desmos.com/calculator/wniskbh3hy

Answer 2

a quadratic intersecting with linear is something we can solve without graphing

or a calculator (I don't have TI calculator)

setting g(x)=f(x)

multiplying by 7

x²-(21/2)x+7=0

x₁=(21/4)+[√((441/4)-28)]/2

calculate and plug into g(x) to find y₁

x₂=(21/4)+[√((441/4)-28)]/2

calculate and plug into g(x) to find y₂