Find the coordinates of the vertex and the intercepts of the following quadraction function. When necessary, approximate the x – intercepts to the nearest tenth.
r(x)=-3x^2-3x-2

Question

Find the coordinates of the vertex and the intercepts of the following quadraction function. When necessary, approximate the x – intercepts to the nearest tenth.
r(x)=-3x^2-3x-2

scarlettfarra2000 · Answer

A quadratic function is a function of the form f(x)= ax^2+bx+c where a, b, and c are real numbers anda≠0. For the given functions a=-3 b=-3 and c=-2
The vertex occurs at x=-b/2a to find the x- coordinate of the vertex of the given functions, substitute the values of a and b into the expression and simplify Let a=-3 and b=-3 simplify 
x=-b/2a=-3/2(-3) =-3/6
The vertex has an x – coordinate of -3/6. To find the y – coordinate, we evaluate r(-3/6)
$$r(-\frac{ 3 }{ 6})=-3(-\frac{ 3 }{ 6 })-3(-\frac{ 3 }{ 6 })-2=\frac{ 11 }{ 36}$$
The vertex would be $$\frac{ 11 }{ 36},-\frac{ 3 }{ 6 }$$

scarlettfarra2000 · Answer

@Atrineas

atrineas · Answer

Idk how to use the equation thing xD but yeah i think that would be it but flip your vertex around cause (x,y) and -3/6 is your x when 11/36 is y

scarlettfarra2000 · Answer

Nope

atrineas · Answer

@TheSmartOne please help

scarlettfarra2000 · Answer

@jim_thompson5910 if your not busy could you please help me

scarlettfarra2000 · Answer

I can't figure out where I did something wrong

atrineas · Answer

@satellite73  can you help her if you have the time please vertex needs to be in fraction and simplified if possible

fortytherapper · Answer

I have not did the math, but....
For the first part of plugging in -3/6

$$-3(\frac{ -3 }{ 6})-3(\frac{- 3 }{ 6 })-2$$

Did you square the first part?

scarlettfarra2000 · Answer

to answer you question @FortyTheRapper  I did but don't know if I did it right or not

fortytherapper · Answer

I got something different:

-3/6 is the same thing as -1/2,  which is the same thing as .5

$$(x,y) \rightarrow (-\frac{ 1 }{ 2 },y)$$

So I would evaluate

$$y = -3(0.5)^2-3(0.5)-2$$

scarlettfarra2000 · Answer

Here's the whole problem because I'm thinking we're suppose to get fractions that's why I've got it wrong the last three or four times (And ignore what I put in the box it's wrong anyways)

fortytherapper · Answer

It says integers or fractions, so either will work

Also, -3/6 should be first, since that's your x value

scarlettfarra2000 · Answer

Okay

scarlettfarra2000 · Answer

But would 0.5 be the y?

fortytherapper · Answer

It would be the x, and negative. As you said in the first response:

"The vertex occurs at x=-b/2a to find the x- coordinate of the vertex of the given functions, substitute the values of a and b into the expression and simplify"

scarlettfarra2000 · Answer

right

scarlettfarra2000 · Answer

Now how do we find the y?

fortytherapper · Answer

We plug .5 into the equation that was given

scarlettfarra2000 · Answer

$$-3(0.5)-3(0.5)-2 = 0.15(2)-0.15(2)$$ because you still have to add 2 both times right?

fortytherapper · Answer

Remember for the first -3(0.5), you have to square the 0.5 first then multiply by -3

scarlettfarra2000 · Answer

So it'd become $$-3(0.25)-3(0.25)-2=-0.75-0.75-2?$$

fortytherapper · Answer

Almost got it

But you squared the second 0.5, when you should have just squared the first 0.5, which means you have this so far:

$$y=-0.75-3(0.5)-2$$

After you calculate the middle term, we can just do simple subtraction and get a Y value

scarlettfarra2000 · Answer

okay so it'd be $$(-\frac{ 3 }{ 6 }, 1.5)$$

fortytherapper · Answer

No, because

$$-0.75-3(0.5) -2 \neq1.5$$

fortytherapper · Answer

First, do 3(0.5)

fortytherapper · Answer

Then you can subtract after finding that value

scarlettfarra2000 · Answer

the answers been in front of my face the whole time haven't it?

fortytherapper · Answer

Somewhat, we just have to multiply 3 and 0.5 in order to get to the last step

scarlettfarra2000 · Answer

1.5

fortytherapper · Answer

Correct, now we can find the answer

$$y = -0.75-1.5-2$$

scarlettfarra2000 · Answer

-2.75 or -0.5?

fortytherapper · Answer

Subtract it one step at a time

I would do -1.5-2 first, then subtract 0.75 from that answer to get the y value

scarlettfarra2000 · Answer

you get 4.25

fortytherapper · Answer

Yep good job, and that's negative. So the answer is (-0.5, -4.25)

scarlettfarra2000 · Answer

Okay let me see and there's going to be two more parts after this one

scarlettfarra2000 · Answer

It's says it's wrong too

fortytherapper · Answer

I see how it is, I forgot the negative. Mb, lemme fix it real quick for you. Sorry

scarlettfarra2000 · Answer

it's okay

fortytherapper · Answer

Since you understand it all, I'll just say

$$y = -3(-0.5)^2-3(-0.5) - 2 = -0.75 + 1.5-2 = 0.75$$

So the answer should be

$$(-0.5,0.75)$$

scarlettfarra2000 · Answer

No it's wrong again the answer is $$(-\frac{ 1 }{ 2 }, -\frac{ 5 }{ 4 })$$

fortytherapper · Answer

Ima have to disagree with MathXL on this one, because I don't see how it can be that

scarlettfarra2000 · Answer

I know how you feel well it's okay I got the rest right now I've got to restart a whole new problem because I can't go on until all problems are 100%

fortytherapper · Answer

I'll rework this one and see what the problem is, if there even is one

scarlettfarra2000 · Answer

you don't have to it's fine

fortytherapper · Answer

I must, I'm one of those people T_T

scarlettfarra2000 · Answer

Alright it's mostly up to you but thank you for all your help