Connecting graphs and equations the curves on the graph...

Connecting Graphs and Equations The curves on the graph below are the graphs of the three curves given by $$ \begin{array}{l}{y_{1}=4 x+5} \\ {y_{2}=x^{3}+2 x^{2}-x+3} \\ {y_{3}=-x^{3}-2 x^{2}+5 x+2}\end{array} $$ (a) Write an equation that can be solved to find the points of intersection of the graphs of $y_{1}$ and $y_{2}$ (b) Write an equation that can be solved to find the $x$ -intercepts of the graph of $y_{3}$ . (c) Writing to Learn How does the graphical model reflect the fact that the answers to (a) and (b) are equivalent algebraically? (d) Confirm numerically that the $x$ -intercepts of $y_{3}$ give the same values when substituted into the expressions for $y_{1}$ and $y_{2}$ .

Transcript

00:04 So what you want to do is you want to solve the following question.

00:07 Who says that? given y one, y 2 and y three is the following.

00:11 Write an equation that can be solved to find the point of intersection of the grabs of taiwan and white.

00:18 So we want to write an equation that souls to find the intersection of highway.

00:23 So what do you have to do to find the intersection of two? find the intersection uh y one and y two.

00:37 What we have to do is we just set why i want to be quantified.

00:42 So what they give us is that four x plus five must be equal to x cube plus two xs square minus x plus three.

00:54 So let us bring everything to one side.

00:56 So that would imply that four x plus five minus excuse -2 access square plus 6 -3 must be zero.

01:08 So let us uh equals the like and items.

01:11 So there is no time that he quotes that is therefore excuse.

01:14 So we'll just keep excuse as it is and as x cube there's nothing except for two minus two x.

01:20 S square four x plus access plus five x five ministries to this is equal to zero.

01:30 So this is an equation was was if we sold this then we find the intersection of my one writer that answers the first question to let us go the second question write an equation that can be sold to find the x intercepts of the graph of vital.

01:52 So why tree is that? so to find the x intercept of white treat.

01:58 So this next question is to find an equation for us? x intercept.

02:08 Okay.

02:10 Right.

02:12 Remember if i have a function why equal to four fix? what do you find the intercept to find x intercept? sure resect.

02:28 Thanks for the year.

02:30 This is what we do here.

02:32 So we set why 3- zero.

02:38 So what this implies is that minus x cube -2.

02:45 Access square plus five x plus two equals to zero.

02:51 This is an equation.

02:52 We solve the situation then we get the x intercept of white.

02:56 That answer the second question writing to learn how does the graphical model to reflect the fact that the answers to and be are equivalent algebraic? okay, so how does the graphical model prepared answers? so basically graphical model would suggest that what do you what do you want to do is if we do what you want equal do i do? all right.

04:48 So what we're really doing is so what i'm really doing is is basically doing why one minus? why do we call the zero? so what the graph of why 1 -62 is so let's say what you want minus why do is some function effects which is value that we do not move.

05:08 So what we're doing is we're really setting effects to this europe.

05:11 So what does this means that it's a graph of effects is something like this when they just three roads are coming.

05:21 So then it looks like this.

05:24 So what we're doing is this is effects.

05:27 So what they're really doing is we're really finding the x intercept is that the x intercepts this is a this is the the sea so a b and c...

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