Help, will fan and medal. need someone to teach me please!

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Help, will fan and medal. need someone to teach me please!

Mathematics
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What is the equation of the following graph?
@LynFran can you help me with this? please
@Robert136 can you help?

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Other answers:

you know the vertex so that makes it easier
i dont know the vertex...i dont get these at all.
owait do you need the quadractic or both the quadratic and the dotted line...
idk..its something to do with ellipses, parabola, or hyperbola...that what the section was about
i can help with the parabola, not sure about that line though
What is the directrix? y=??
What is the vertex? You need both them to write out the equation. Please, answer.
the vertex is (1,4)
whats the directrix.... i dont think ive learned those
The red line below to the graph is a directrix
if you don't know that method, ok, pick 3 points on the graph. Please.
y = 3
thats the directrix
Now, what method do you want me to follow?? directrix method or standard one?
which one do u think would be the easiest to understand?
Depend on you. I am ok with both
Standard one, ok?
okay
what is the standard form of a parabola?
y=ax^2+bx+c
YYYYYYYYYYYYYES
now, 3 points Vertex (1,4) you pick other two.
just 2 random points?
Yes, but for convenience, you should pick the point whose coordinates are integers like (-1,5). Got what I meant?
so the points where the red line cross over?
no, the point on the parabola
like (3,5)
Yes,
Now, starting Vertex \((\color{red}{1}, \color{blue}{4})\) Plug them into the standard form like \(\color{blue}{4}= a\color{red}{1^2}+b\color{red}{1}+c\) you have 4 = a +b +c, right? name it as (*) Do the same with other two point, what do you get?
im lost.. im sory. my computer froze sorry about the late anwser
5=a-b+c 5=5a+5b+c
@Loser66 am I understanding it?
5=a -b +c, yes but for (3,5) it is not right 5 = a(3^2) +b(3) +c , that is 5= 9a +3b+c
Now, you have 3 equations, 3 unknowns a, b, c. You can solve for them a + b + c = 4 (*) a - b + c = 5 (**) 9a + 3b + c = 5 (***)
Take (*) -(**) , what do you get?
-1
so i have -1 left, and 9a + 3b + c = 5
|dw:1439603548746:dw|
Take (***) -(**)
8a + 4b
|dw:1439603653405:dw|
Replace a = 1/4, b = -1/2 in (*) you get c = ??
c=4.25
yes, or 17/4 Now, plug back to standard form, y = ax^2 +bx+c . that is your answer.
y=ax^2+bc+17/4?
a = 1/4 b= -1/2 c = 17/4 Plug in \(y= ax^2+bx +c\)
okay thank you. can i tag u if i have anymore questions? i like tht ur showing me instad of telling me
HI!!
there might be a somewhat easier way to get this, using two points although above method certainly works
thank you. im sure ill run into more of these, do u mind if i tag u if i need help?

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