Quadratic Equations # The 3 Parabola Forms: Standard Form, Vertex Form and Factored Form.

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2x

= 2(x

= 2(x-4)*(x-2) since (-4) + (-2) = -6 and (-4)*(-2)=8

That’s all 😉

Standard Form:

y = ax²+bx+cVertex Form:

y = a(x-h)²+k(h,k) = Vertex Coordinates.

Factored Form:

y = a(x-r)(x-s)r and s = Zeros of the Parabola.

Standard Form:

y = x²+6x+8can be rewritten in Vertex Form:

y = (x+3)²-1It tells us that above Parabola has Vertex Coordinates = (3,-1).

The process to convert from Standard Form to Vertex Form is called “Completing the Square”. You can Complete the Square for your quadratic equation here:

/solve-a-quadratic-equation-by-completing-the-square/

Factored Form:

y = (x+4)(x+2)It tells us that above Parabola has Zeros -4 and -2 .

The process to convert from Standard Form to Factored Form can be done here:

Or simply use the head menu when converting between the different Parabola Forms.

y=a(x-h)²+kwhere

The Standard form of a Parabola is

y=ax²+bx+c

we first apply the binomial formula to expand and get

Next, we distribute the 2 to get

With 2-5=-3 we finally arrive at the Standard Form:

In general, we obtain the Standard Form from the Vertex Form by using these 2 steps:

Given:

Step1: (Use Binomial Formula)

Step2: (Distribute and Combine 2 like terms ah² and k)

We created a separate page for you that teaches the Vertex to Standard Form Conversion. It also has a Solver that allows you convert you Vertex Form Equation into Standard Form. Visit our page here.

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