Question

The graph of a function is a parabola that has a minimum at (-1,-2) and goes through the point (0,1).

What is the equation of the function in standard form?

Substitute numerical values for a, b, and c.

y=ax^2+bx+c

Answer 1

Have a great rest of ur day :)

Explanation:

Answer 2

y = 3x^2 + 6x + 1

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