Answer:
y = 3x^2 + 6x + 1
Step-by-step explanation:
We're given two points on the graph: (-1, -2) and (0, 1).
The pertinent equation is
y=ax^2+bx+c, but the vertex form would also be useful: y - k = a(x - h)^2.
Note that this parabola opens up, and that the minimum point is also the vertex: (-1, -2).
The vertex is (-1, -2), and so: y + 2 = a(x + 1)^2, and
the graph goes through (0, 1), so we can rewrite y + 2 = a(x + 1)^2 as
1 + 2 = a(0 + 1)^2, or:
3 = a(1)
So now we know that a = 3 and that the equation of this parabola in vertex form is y + 2 = 3(x + 1)^2
Lastly we must put the above result into standard form. To do this, perform the indicated multiplication.
y + 2 = 3(x^2 + 2x + 1) = 3x^2 + 6x + 3
Writing y on the left and all the rest on the right, we get
y = 3x^2 + 6x + 1
