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Quadratic Project Modeling Algebra Section 11009

Quadratic Project Modeling Algebra Section 11009. Juvenile Violent Crime Arrests. Source: http://wps.prenhall.com/esm_lehmann1/51/13153/3367376.cw/-/3367383/index.html. Scatter Plot of Data. # of Juvenile Arrest. Years x=number of years after 1988. Why is this a Quadratic Function?.

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Quadratic Project Modeling Algebra Section 11009

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  1. Quadratic ProjectModeling Algebra Section 11009

  2. Juvenile Violent Crime Arrests Source: http://wps.prenhall.com/esm_lehmann1/51/13153/3367376.cw/-/3367383/index.html

  3. Scatter Plot of Data # of Juvenile Arrest Years x=number of years after 1988

  4. Why is this a Quadratic Function? • This data represents a quadratic function because the second differences of the “Juvenile Arrest” are very close to being equal which makes this a parabola • The Scatter Plot also forms almost a perfect parabola which makes the data quadratic

  5. How to Find Equation • To find equation use the Quadratic Regression Feature on calculator • Ax2+Bx+C=0 • F(x)= -6.5x2+70.3x+320

  6. F(x)= -6.5x2+70.3x+320 • This equation is a maximum because the leading coefficient is negative • Finding the Vertex: • Use formula: -b/2a • -70.3/2(-6.5)= -70.3/-13 • X=5.41 • Plug in X to the original equation to find Y • F(5.41)=-6.5(5.41)2+70.3(5.41)+320= • -190.24265+380.323+320= 510.1=Y • VERTEX= (5.41, 510.1) • This means in the year 1993 (5.41+1988) there were 510.1 juvenile crime arrests

  7. Finding Horizontal Intercept • To find horizontal intercept the Y value must be 0 • (0)= -6.5x2+70.3x+320 • To find solution use Quadratic Formula • -b+- 2ac • -70.3+- • There are no juvenile arrests in the year 1984 and 2002. This works with our data b2-4ac 42 (-6.5)(320) 2(-6.5) X=14.26, -3.5

  8. Finding Vertical Intercept • To find vertical intercept X value must be 0 • F(x)= -6.5x2+70.3x+320 • F(0)= -6.5(0)2+70.3x+320 • Y= 320 • In the year 1988 the number of juvenile arrests is 320 which is seven off from the data, the original data states in the year 1988 there are 327 juvenile arrests

  9. Quadratic Parabola of Data # of Juvenile Arrest Years x=number of years after 1988

  10. Predictions Made with Equation • The model can be used to find the number of juvenile arrests when no data was collected • Year 1991= F(3)= -6.5(3)2+70.3(3)+320= 227.6 arrests • Year 2000= F(12)= -6.5(12)2+70.3(12)+320= 472.4 arrests

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