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 $\displaystyle -\frac{b}{2a}$. So you have:
$\displaystyle -\frac{b}{2a}=1 \Longleftrightarrow b = -2a$
The coordinates of the given points must satisfy the equation of the function. Plug in the coordinates:
$\displaystyle 1=a \cdot 0^2+b \cdot 0 + c \Longleftrightarrow c=1$
$\displaystyle -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