# Math 11-Equation of Quadratic Function, when given vertex and other point on parabola

• Aug 7th 2009, 09:01 PM
MastiffLover48
Math 11-Equation of Quadratic Function, when given vertex and other point on parabola
Hi! I have this Math 11 problem. I do my math through Distance Ed. and there are no examples like this one in the supplied lessons. If anyone could help me with this question, that would be great!
The problem statement, all variables and given/known data

Find the equation of the quadratic function with a vertex at (1,3) passing through the points (2,1). Write your answer in the form y=ax^2+bx+c.

The attempt at a solution

Using these two points (one being the vertex), I am able to write an equation, but in the form of y=a(x-h)+k. Below is the answer I get for that:
y=-2(x-1)+3
However, I was wondering if I can just convert this answer to the other quadratic form, or do I have to do the question an entirely different way.
Any comments/help on ways to do this question appreciated. (Nod)
Thanks,
MastiffLover48
• Aug 7th 2009, 09:21 PM
malaygoel
Quote:

Originally Posted by MastiffLover48
Hi! I have this Math 11 problem. I do my math through Distance Ed. and there are no examples like this one in the supplied lessons. If anyone could help me with this question, that would be great!
The problem statement, all variables and given/known data

Find the equation of the quadratic function with a vertex at (1,3) passing through the points (2,1). Write your answer in the form y=ax^2+bx+c.

The attempt at a solution

Using these two points (one being the vertex), I am able to write an equation, but in the form of y=a(x-h)+k. Below is the answer I get for that:
y=-2(x-1)+3
However, I was wondering if I can just convert this answer to the other quadratic form, or do I have to do the question an entirely different way.
Any comments/help on ways to do this question appreciated. (Nod)
Thanks,
MastiffLover48

What you have got is a straight line.

You are required to find $y=ax^2+bx+c$
and you are given only two points...hence it is difficult to determine a,b, and c.

But it is given that (1,3) is a vertex point. Do you know what does it mean?
At vertex, x=-b/2a......................(1)

With the help of eq(1) and another point(2,1), you easily find a,b and c.
• Aug 7th 2009, 09:22 PM
songoku
Hi MastiffLover48

The equation should be : $y=a(x-h)^2+k$
• Aug 7th 2009, 09:27 PM
malaygoel
Quote:

Originally Posted by songoku
Hi MastiffLover48

The equation should be : $y=a(x-h)^2+k$

here (h,k) is the vertex.
• Aug 8th 2009, 10:37 AM
MastiffLover48
Hi! Thanks for all the comments! (Happy) I used the equation that I had:
y=-2(x-1)^2+3
and then factored it, which I ended up with an answer of:
y=-2x^2+4x+1
Does that seem correct to you?
Thanks,
MastiffLover48
• Aug 8th 2009, 07:04 PM
songoku
Hi MastiffLover48
Quote:

Originally Posted by MastiffLover48
Hi! Thanks for all the comments! (Happy) I used the equation that I had:
y=-2(x-1)^2+3
and then factored it, which I ended up with an answer of:
y=-2x^2+4x+1
Does that seem correct to you?
Thanks,
MastiffLover48

(Yes)