# Thread: find b and c

1. ## find b and c

Help please.
Find b and c so that y=13(x^2)+bx+c has a vertex (3,-2).

so b=______
and c=_____

2. Hello, lsnyder!

Find $b$ and $c$ so that $y\:=\:13x^2+bx+c$ has a vertex (3,-2).
We're expected to know that the vertex is at: . $x \:=\:\frac{-b}{2a}$

So we have: . $\frac{-b}{2(13)} \:=\:3 \quad\Rightarrow\quad b \:=\:-78$

. . and the equation is: . $y \:=\:13x^2 - 78x + c$

Since (3,-2) is on the graph: . $-2 \:=\:13(3^2) - 78(3) + c \quad\Rightarrow\quad c \:=\:115$

Therefore: . $\boxed{b \:=\: -78}\quad\boxed{ c \:=\:115}$