General form equation of parabola

Question

Write the general form equation of the parabola passing through P with vertex V

v: (1,3)

p: (-2,-6)

please show each step, I don’t understand, thank you.

Answer 1

Vertex is the max point, if another point is lower.

It's a downward opening parabola.

General form of the equation would be y-k=a(x-h)² with (h,k) as the vertex

which is (1,3) h=1, k=3. All we need now is a, which we can find

using that other point (-2,-6)

The equation is y-3=a(x-1)² now substitute x=-2 and y=-6 into that equation to solve for a

-6-3=a(-2-1)²

-9=a(9)

Give me another day to rethink this through. This is my first reaction, within minutes.

a=-1

so final equation is y-3=-(x-1)²

That becomes y=x²-2x+4

maybe, if I haven't made a mistake somewhere, it's always possible.

check with other answers. Mistakes are very common. Some instructors

do it right in class. But it's not their lack of talent, often more than overconfidence

due to their very real talent. Maybe.

Answer 2

To solve problem we use vertex form y = a(x-h)² + k, (h,k) = (1,3) is vertex;

then y = a(x - 1)² + 3. To get a we use fact that point (-2,-6) is point of parabola

because -6 = a(-2 - 1)² + 3, 9a = -9, a = -1.

We have y = -(x - 1)² +3 or y = -x² +2x + 2.

This is general form: y = -x² + 2x + 2