Question

For the function 𝑦𝑦 = −2𝑥𝑥2 + 4𝑥𝑥 + 1, what are the coordinates of the vertex? Is it a maximum or
minimum point? Hint: use the vertex/axis of symmetry formula for 𝑥𝑥. Show all work algebraically to
earn full credit and use Desmos only to check your answer.

Answer 1

y=2x^2+4x+1 **

Answer 2

One moment, I got it.

Answer 3

do you know this :

if f(x) = ax^2 +bx +c so the vertex is (-b/2a , f(-b/2a) )

Answer 4

That is not right jhonyy

Answer 5

The vertex is (-1, -1)

Answer 6

It is a minimum value @Razor

Answer 7

\[f(x) = ax^2+bx + c \] ?

Answer 8

So here, let me write this all down: Vertex is at (-1, -1), and it is a minimum point.

Answer 9

That is standard form, what am I supposed to do with it?

Answer 10

Uhm, I'm supposed to have all the steps. Like how did you get to (-1,-1) ?

Answer 11

using my posted formula you get these value too

Answer 12

^

Answer 13

OOOOOOOOOH, ok

Answer 14

hahaha, I am used to doing math in my head

Answer 15

Srry about that

Answer 16

so do I just have to add the following equation I was given? Or graph it

Answer 17

Try graphing it first.

Answer 18

I will get the steps in a moment

Answer 19

@Razor you need learn this formula posted above

Answer 20

Yes, use johnyy's formula.

Answer 21

using this formula you can calcule the vertex of a quadratic

Answer 22

and how you decide that is minim or maxim ? just in this case bc. the vertex is (-1,-1) so give the value of 0 to x and so in this way for f(0) what value will get ?

Answer 23

I'm really not sure I'm sorry. Math is my nemesis

Answer 24

You can determine which is the maxim or minim based on the shape of the graph. For example: A graph in a "u" shape (like the one in this problem) The vertex is the point where it rounds at and changes direction. Since it is an up u, it would be a minimum, because of how low it is on the graph. Rather than if we had an "n" shape, where the vertex would be the highest, making it a maxim... Hope this helped!

Answer 25

Depends on the value of a if a >0 then minimum cuz opens up
if a <0 then opens down or maximum

Answer 26

exactly @darkknight

CONGRATS !!!

Answer 27

I am the darkknight

Answer 28

Yeah, that's my simplified explanation XD

Answer 29

@Razor , if you need your work shown: https://symbolab.com it will get all the work you need, because it is step by step calculator.

Answer 30

Yeah so if the line is positive it's a minimum, someone told me if it was negative it'd still be minimum

Answer 31

Unless it was a typo then it'd be maximum

Answer 32

Okay, I think I got it. abc. a = 2, b = 4 and c = 1

Answer 33

Which was super obvious but I didn't know if I was right or not until I look at it

Answer 34

so a is -2, which means that is opens down and it is a maximum

Answer 35

Does it determine if it's maximum or minimum by "a" and not the rest of the variables?

Answer 36

yes,

Answer 37

Hmm. I would look this up. I don't remember learning that.

Answer 38

\[x _{v} =-\frac{ 4 }{ 2*2} \]

Answer 39

Like that and then simplify

Answer 40

Yes, good job

Answer 41

Sweet, I think I got it from here. Thanks, guys. Sorry for dragging that out longer than it needed to be

Answer 42

No worries! I enjoy helping. And doing nerdy problems HAHAHA

Answer 43

XD