Quadratic Models  Quadratic Models- Models based on quadratic functions  Acceleration Due to Gravity- The acceleration of a free-falling object toward.

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Quadratic Models

 Quadratic Models- Models based on quadratic functions  Acceleration Due to Gravity- The acceleration of a free-falling object toward another object caused by gravitational forces; on the surface of the Earth equal to approximately 32 feet or 9.8 meters per second per second  Quadratic Regression- A technique that finds an equation for the best-fitting parabola through a set of points  Impressionistic Models- A model where no theory exists that explains why the model fits the data, also called ‘non-theory based model’

 F(x)=Ax 2 +Bx+c  A≠0  x is the independent variable  F(x), also known as y, is the dependent variable

This will find solutions to ax 2 +bx+c=0

 Y-intercept- the value for C  X-intercept- Use the quadratic formula

 Sketch a graph from a≤x≤b  For every integer a to b, plug in each point into your equation (should be substituting value in for x and solving for y)  Ordered pair that you get as an answer should be plotted out  When all ordered pairs are plotted, connect all points with a line, with arrows continuing in both directions

 Graph function on your calculator  Press 2 ND, then CALC (TRACE) ◦ Depending on what parabola looks like  Select Option 3:Minimum  Select Option 4:Maximum  Select bounds to the left and right of where you think the min/max is ◦ If finding minimum, than all values of y are ≥ min. ◦ If finding maximum, then all values of y are ≤ max.

Minimum Maximum

 F(x)=Ax 2 +Bx+C  If A is positive, then the graph opens upwards and has a minimum value  If A is negative, then the graph opens downward and has a maximum value

 H=-16t 2 +vt+s  H=height  t=time  v= initial velocity  s= initial height

 Plug in values for initial velocity, in for v, and initial height, in for s  Plug in given time in seconds for t  Solve for H

 Graph equation in your calculator  Find where y=0  X-value is solution

 Worksheet 2-6