The graph of the function f(x)=ax^2+bx+c has its vertex at (0,1) and passes through the point (1,9) find a b and c

The equation of a parabola is , where (h,k) represents the vertex.

The values of a, b and c are 8, 0 and 1, respectively.

We have:

--- the vertex

--- the point it passes through

Substitute in

Substitute in

Collect like terms

Substitute in

So, the equation of the parabola is:

Compare to

See attachment for the equation of

Read more about equations of parabola at:

link

Step-by-step explanation:

The vertex form of a quadratic is where the vertex is .

We are given .

Plugging this in gives us:

Simplifying:

Since it passes through , we can use this information to find .

So the quadratic in vertex form is .

That happens to be in standard form as well.