Equation of a Function with vertex (2,3), passing thru (0,2)

[Ironhawk]

I have to find the equation of a fuction that has a vetex of (2,3) and passes through the point (0,2). How do I go about solving this problem? Thank you.

 

[chivox]

I would start by looking in the book that you have for your class. There is probably a section entitled, "Finding the equation of the quadratic," along with a subsection entitled, "When you know the vertex and one point on the graph."

If that is not enough free math help, please write back and tell us what you have come up with so far. I think it's more important to understand the process than this particular solution. Think about what you know about this function (the vertex will give you h and k, and the point will give you a, in the general form of the equation). Note that there are an infinite number of equations that would result in a function that passes through those two points. We need more from you if we have a shot at providing any help at all.

If you need more help, please write back, but you have to show us what you have done so far with this problem. If you tell us exactly where you're stuck, we'll be right on top of it.

 

[Ironhawk]

I have to find the equation of a fuction that has a vetex of (2,3) and passes through the point (0,2). How do I go about solving this problem? Thank you.

I have researched and came up with the equation f(x)=a(x-h)^2 +k
Y=a(x-h)^2 +k
2=a(0-2)^2+3
2=a(-2)^2
-1=a(4)
-1/4=a(4/4)
a=-1/4

y=1/4(x-2)^2=3

Is this right or am I going in the wrong direction?

 

[chivox]

...

Y=a(x-h)^2 +k
2=a(0-2)^2+3
2=a(-2)^2
-1=a(4)
-1/4=a(4/4)
a=-1/4

y=1/4(x-2)^2=3

Is this right or am I going in the wrong direction?

Now we're talking. Except it's hard to follow your work when you leave out the "3" for k on the third line above. You still haven't subtracted it from the left at that step, so why have you shown it disappearing from the right-hand side? Anyway, I leave the completeness of your work to you. That looks right.

-Paul

 

[Ironhawk]

I have to find the equation of a fuction that has a vetex of (2,3) and passes through the point (0,2). How do I go about solving this problem? Thank you.

I have researched and came up with the equation f(x)=a(x-h)^2 +k
Y=a(x-h)^2 +k
2=a(0-2)^2+3
2=a(-2)^2
-1=a(4)
-1/4=a(4/4)
a=-1/4

y=1/4(x-2)^2=3

Is this right or am I going in the wrong direction?

ok, lets try this again.

2=a(0-2)^2+3
2=a(-2)^2+3
2=a(4)+3 then subtract -3 from both sides
-1=a(4) then divide both sides by 4 to get ride of the 4 from the right side
a=-1/4 just flip it around.

y=-1/4(x-2)^2+3 answer

did I get it this time? -2 x -2 is positive 4

 

[chivox]

Beautiful. (Technically speaking, "clear, complete, and logical.")

 

[Ironhawk]

Beautiful. (Technically speaking, "clear, complete, and logical.")

Thank you, you been a great help! I see your going to make me work all the way! lol Thanks again.

 

[mmm4444bot]

... I see your [sic] going to make me work all the way ...

So will your employer(s), once you enter the real world (where mommy and daddy are no longer available to lead you around by the hand).

Cheers,

~ Mark

PS (FYI): It would probably be wise to stop using the letter x as a multiplication symbol. Unless you are expressing scientific notation, it tends to be confusing. Instead, indicate multiplication using an asterisk or grouping symbols, as in 4*5 or (4)(5).