1. ## constructing polynomials

Qs. Write down a quadratic polynomial with a minimum value of 3 when x=2, and P(0)=15

im not looking for the answer here, i would jst realli like to no how to get there and the processes of working these kind of questions out
thanks so much for any help given =D

2. Originally Posted by THSKluv
Qs. Write down a quadratic polynomial with a minimum value of 3 when x=2, and P(0)=15

im not looking for the answer here, i would jst realli like to no how to get there and the processes of working these kind of questions out
thanks so much for any help given =D
assume
$\displaystyle P(x)=ax^2+bx+c$

with conditions given is problem, determine a,b,c.

3. Originally Posted by THSKluv
Qs. Write down a quadratic polynomial with a minimum value of 3 when x=2, and P(0)=15

im not looking for the answer here, i would jst realli like to no how to get there and the processes of working these kind of questions out
thanks so much for any help given =D
The standard for of a quadratic:

$\displaystyle a(x+\frac{b}{2a})^2-\frac{b^2}{4a}+c$

Can you see what needs to be done?

4. I like the following method better...

Use the vertex form of the quadratic:
$\displaystyle P(x) = a(x - h)^2 + k$
where (h, k) is the vertex. The vertex is the minimum or maximum value of the parabola, so plug (2, 3) in:
$\displaystyle P(x) = a(x - 2)^2 + 3$

You're also given that P(0) = 15, so plug in 0 for x and 15 for P(x), and solve for a:
$\displaystyle 15 = a(0 - 2)^2 + 3$
...

I'm sure you can figure out the rest.

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