Intersecting Polynomial functions

Introduction

Here given the function of parabola, f(x)=(2x^2-3x+4)/2 and the equation of line is g(x)=x/2+1. so, from this applet we have to find out the intersecting points of parabola and a line also visualize it in graphics.

objectives

Intersect the parabola f(x)=(2x^2-3x+4 )/2 with the line g(x)=x/2+2 by using CAS in geogebra also visualize it in graphics.

User Guidelines

-At first, given parabola is f(x)=(2x^2-3x+4)/2 and line is g(x)=x/2+2 then to find the intersecting points of the parabola and line you should input parabola in CAS by f(x):=(2x^2-3x+4)/2 and input line by g(x)=x/2+2(by using keep input tool). -Then define a function h(x):=f(x)-g(x)(by keep input tool). - Enter h(x)=0 and apply solve tool then you get the x-coordinates of intersecting points which are:-(0,0) and (2,0). -Now,calculate the intersecting points by using command intersect by this, s:=intersect[f(x),g(x)].then you get the two intersecting points (0,2)and (2,3) between the parabola and line .which is the required solution. then click on graphics and click on all input in the CAS you get graphics also.

Materials(you can put another equation of parabola and a line to find the intersecting points between them)

Check your understanding

Q.n Which of the following pair of points are the intersecting points of the parabola and line?

Select all that apply

A
i)(0,0) and (2,0)
B
ii)(0,2)and (2,3)
C
iii)(2,3)and (0,0)
D
iv)(2,1)and (0,0)

Construction Protocol

1.Open a new GeoGebra window. 2.Switch the perspective-CAS. 3.Define a function f as f(x):=(2x^2-3x+4)/2 (by keep input tool) 4.Again define a function g as g(x):=x/2+2 (by keep input tool) 5.Define a function h as h(x)=f(x)-g(x). 6.Enter h(x):=0 and apply solve tool it helps to obtain the x-coordinates of intersecting points. 7.calculate the intersection points by using command intersect as s:=[f(x),g(x)]. it gives the intersection points between the parabola and line.