Please please pleaseeeee help me with these problems!!! ?

Question

i need help with my math homework. here are my 3 questions:

1. true or false-the graph of a linear equation can have either no x-intercepts or only one x-intercept. justify your answer.

2. think about it. find a and b if the x-intercepts of the graph of y= (x-a)(x-b) are (-2,0) & (5,0)

3. explain how to find an appropriate viewing window for the graph of an equation.

please try to explain things so that its easy to understand. it would be very much appreciated!! thank you :]

Answer 1

i'll give you a hint - y=(x-a)(x-b) has the x-intercepts of (-2,0) and (5,0). How many intercepts is that?

i'm not sure about no. 2, but if i were you i would try plugging the x-intercepts into the equation.

for three, is it a calculator?

I don't want to give you the answers but i do wanna help.

Answer 2

1. true because if it has two x-intercepts it is no longer a linear equation but a parabola, or another power function that is greater than one. like if it has too roots (x intercepts) that means that x has a power of two or higher, linear equations have a power of only 1.(i.e. the x is raised to the first power.

2. This is actually not so hard if you don't think too much. You are given an equation and two points, which will help you solve for a and b. First we will use the point (5,0) and plug it into the equation making it: 0 = (5-a)(5-b). It looks like we are stuck because we don't have a numerical term for a or b. however that is where the thinking comes in. in mulitplication, the ONLY way to get a number equal zero is to multiply it by zero. even if it just one number. now look back at the plugged in equation. what is a way to get one of the (5-a/b) to equal zero? By by putting a 5 in either the a slot or the b slot. but only one. because no matter what the other number is, since one of the numbers equal zero, the equation will in the end equal zero. now let's say that we put 5 in the place of 'a' that will make the equation read: 0= (5-5)(5-b), and that will equal zero.

Now wait we aren't done, since we have to deal with b, that is where the other point (-2,0) comes in. You know what a is so now rewrite the equation so that x = -2. it should read: 0= (-2-5) (-2-b). alright, there are two ways you can go about this. one way is to solve for 'b':

0= -7(-2-b) (divide both sides by 7 becuase it is bound by muliplication adn you need to use the opposit operation to get it to the other side. 0/7 is 0)

0 = -2-b (add b to both sides and you get b= -2)

another way to do it is to reapply what i said earlier to with the equation involving the 5. but since i just gave you the answer it doesn't matter anymore so a=5 and b= -2

it could also be the other way around, but i chose it this way. woah that was alot.

3. okay do you use a ti83, ti83 plus, or ti84 calculator? i'm going to presume you do and that is what i am basing this answer on. Okay take your cal out and turn it on. go to the top and go to WINDOWS. Click it and you should already have a default window screen (i.e. Xmin=-10 etc). to find the appropiate window you first need an equation. i'll use x^2+12x+32=y

alright the first thing you should automatically know is your Ymax. 32 is your yintercept, the point that intercects the y axis, so your ymax should be a little larged than your y intercept. so we shall say 40. your y min is usually -10 so keep it that way. your y scale (since you are using 40) should 5. now you need to find the roots of the equation so you can find out what is the perfect x min/max. i'm not going through that whole break down, but the roots of the equation are -4 adn -8, so you know where the equation is: it is on the negative side. so your x max will be 0 (to give some room in your parabola so you can see the picture better) and the x min should be either -10 or -12 and the x scale should be 1 or 2 depending on how you want your graph to look.

There really isn't an exact perfect viewing. it just depends on how big or smal you want your graph to be, but i just gave you the basics above.

I hope i didn't confuse you in anyway. i hope i helped at least a little.