Equation of a parabola?

Question

Vertex: (1,2)
Passing Through: (0,0)

Can you put it in vertex form a(x-h)^2a+k

Answer 1

You're given the vertex:

y = a(x - 1)² + 2

And then (0, 0), has to satisfy the equation, so plug it in:

0 = a(0 - 1)² + 2 = a + 2

-2 = a

So the equation is:

y = -2(x - 1)² + 2

or, if you want to write it out in the other "standard" form:

y - 2 = -2(x² - 2x + 1) = -2x² + 4x - 2

2x² - 4x + y = 0

Answer 2

From the information you have given we have

y - 2 = a(x - 1)²

Plugging in (0,0) we have

0 - 2 = a(0 - 1)²
-2 = a

So the equation of the parabola is

y - 2 = -2(x - 1)²
y = -2(x - 1)² + 2