determine constants

**euclid2** · May 19th 2010, 05:14 PM

Determine values of a,b,c such that the graph $y=ax^2+bx+c$ has a relative maximum at $(3,12)$ and crosses the y axis at (0,1)

**skeeter** · May 19th 2010, 05:48 PM

Originally Posted by euclid2

Determine values of a,b,c such that the graph $y=ax^2+bx+c$ has a relative maximum at $(3,12)$ and crosses the y axis at (0,1)

first, you have two points on the curve given to you ...

(0,1) ... $1 = a(0^2) + b(0) + c$ ... now you know $c = 1$

(3,12) ... $12 = a(3^2) + b(3) + 1$

this gives you the equation $9a + 3b = 12$ , or simplified, $3a + b = 4$

now you need another equation ... relative extrema occur at critical values; in this case where $y' = 0$ .

$y = ax^2 + bx + 1$

$y' = 2ax + b$

$2ax + b = 0$ at $x = 3$ ...

$6a + b = 0$

there is your second equation in terms of $a$ and $b$ ... solve the system.

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