SOLUTION: Vertex (1,2) Point (3,-4) Write the equation of the graph below in standard form y=a(x-h)^2+k and general form y=ax^2+bx+c. I managed to solve for the standard form (which I w

Question 1200626: Vertex (1,2) Point (3,-4)
Write the equation of the graph below in standard form y=a(x-h)^2+k and general form y=ax^2+bx+c.
I managed to solve for the standard form (which I will show) but I am having difficulties transferring it to general form.

-4=4a+2
-2 -2
-6=4a
-- --
4 4

Does that look correct? If so how I mold it into general form?

Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Vertex (1,2) Point (3,-4)
y=a(x-h)^2+k
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------

-

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Looks good so far.
I appreciate you showing your work.

The -6/4 can be reduced to -3/2.

This means the vertex form is

where
a = -3/2
h = 1
k = 2

Let's expand things out (using the FOIL rule) and combine like terms

FOIL rule

Distribute

The equation is now in general form y = ax^2+bx+c, where,
a = -3/2
b = 3
c = 1/2

--------------------------------------
Check:
Plugging x = 1 should lead to y = 2

Therefore, (1,2) is on the parabola.

Plugging x = 3 should lead to y = -4

That confirms (3,-4) is also on the parabola.
--------------------------------------

Graph:

Desmos and GeoGebra are two graphing options I recommend.

Here is the link to the interactive Desmos graph.
https://www.desmos.com/calculator/vz0x6inti1
Next to each equation (on the left side panel) are red and blue buttons. Click each of those to turn off/on the equation curve.
This will help illustrate the two curves occupy the same exact space. They pass through the same set of points.
This is visual confirmation that is the same as

Side note: The value of a = -3/2 is negative, which means the parabola opens downward.

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