Parabola # Parabola Graphing Calculator

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Different equations may produce the same Parabolas.

For example, these 3 equations will graph the same Parabola. Try it below.

Can you create 3 different equations that result in the same Parabola?

Try it above by typing in 3 different equations into the Parabola Graphing Calculator above.

Hint: All 3 equations would be equal when converted to Standard Form.

Read below on how to convert between the 3 Parabola forms.

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). Verify that above on the Graph of the Parabola Graphing Calculator. You can actually click on the vertex and the coordinates will show.

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

Factored Form:

y = (x+4)(x+2)It tells us that above Parabola has Zeros -4 and -2 . Again, verify that above on the Graph of the Parabola Graphing Calculator. You can actually click on the zeros and the coordinates will show.

The process to convert from Standard Form to Factored Form can be done below.

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

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.

(h,k) = Vertex Coordinates.

Example: Vertex=(1,2) which makes the Parabola Equation

Given Point (3,10) turns the Equation to

Therefore, the Parabola Equation is calculated as

If however you are given two Zeros and a Point you will use the Factored Form:

Example: Zeros are 3 and 5 which makes the Parabola Equation

Given Point (4,-2) makes the Parabola Equation

Therefore, the Parabola Equation is calculated as

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