Neil is analyzing a quadratic function f(x) and a linear function g(x). will they intersect? f(x) graph of the function f of x equals x squared plus 2 g(x) x g(x) 1 3 2 5 3 7

neil is analyzing a quadratic function f(x) and a linear function g(x)

f(x)= x^2 + 2

the table g(x) is

x       >   1         2       3

g(x) >   3       5       7

when f(x) and g(x) intersects then f(x) = g(x)

plug in some values for x and find out f(x)

let make the table for f(x). we know f(x)= x^2 + 2

x       >   1         2       3

g(x) >   3       6       11

from both f(x)   and g(x) table we can see that when x= 1 , f(x)=3  

also g(x)= 3

hence f(x) and g(x) intersects at (1,3)

nlgqer

step-by-step

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)