Find a, b and c

The graph of the function f(x) = ax^2 + bx + c has a vertex at x = 1 and passes through the points (0, 1) and (-1, -8). Find a, b and c.

Quote:

Originally Posted by symmetry

The graph of the function f(x) = ax^2 + bx + c has a vertex at x = 1 and passes through the points (0, 1) and (-1, -8). Find a, b and c.

Hello,

to calculate 3 values you need 3 equations. You know that the x-value of the vertex is $-\frac{b}{2a}$ . So you have:

$-\frac{b}{2a}=1 \Longleftrightarrow b = -2a$

The coordinates of the given points must satisfy the equation of the function. Plug in the coordinates:

$1=a \cdot 0^2+b \cdot 0 + c \Longleftrightarrow c=1$

$-8=a \cdot (-1)^2+b \cdot (-1) + c$

Solve for a, b and c. Use the method which is the most convenient for you. I've got:
a = -3, b = 6 and c = 1

EB

ok

I thank you for your help and insight.