4.3 MODELING WITH QUADRATIC FUNCTIONS

WRITING THE EQUATION OF A PARABOLA

When you know the vertex and a point on a parabola you can write the equation of the parabola using vertex form.

If you do not know the vertex, then you can use any three points on the parabola and standard form to write the equation of the parabola.

Given three points on the parabola, what is the equation of the parabola?1. Substitute each point into to write a system

of equations.2. This creates a system with three equations

and three variables, solve the system using the method of your choice

WRITING THE EQUATION OF A PARABOLA

EXAMPLE: FIND AN EQUATION IN STANDARD FORM OF THE PARABOLA PASSING THROUGH THE POINTS

(0,0 ) , (−1 ,−2 ) , (1,6 )

EXAMPLE: FIND AN EQUATION IN STANDARD FORM OF THE PARABOLA PASSING THROUGH THE POINTS

(0,0 ) , (1 ,−2 ) , (−1 ,−4 )

EXAMPLE: FIND AN EQUATION IN STANDARD FORM OF THE PARABOLA PASSING THROUGH THE POINTS

(1 ,−1 ) , (2 ,−5 ) , (3 ,−7 )

COMPARING QUADRATIC MODELS

Campers at an aerospace camp launch rockets on the last day of camp. The path of rocket 1 is modeled by the equation where is time in seconds and is the distance from the ground. The path of rocket 2 is modeled by the graph shown. Which rocket flew higher? Which rocket stayed in the air longer?

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ASSIGNMENT

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Do #16 first!