3.1 Exploring Quadratic Relations “Pop Fly” in Baseball https://www.youtube.com/watch?v=XzpYf07 -1As Hard to catch, since it’s falling straight down It’s modeled by the relation: y = -5x2 + 20x + 1 x: time in seconds after ball leaves the bat Height equation is an example of a quadratic relation in standard form PARABOLA ->

Standard Form Quadratic Relation in Standard Form is a relation in the form: y = ax2+ bx + c, where a ≠0 In the baseball’s height relation: y = -5x2 + 20x + 1 a = -5; b = 20; c = 1

Explore Changes to Standard Form How does changing the coefficients and constant in y = ax2 + bx + c affect the graph of the quadratic relation? http://fooplot.com

Analyzing Further y = -5x2 + 20x + 1 – Make a table of values x y 1st Diff 2nd Diff -3 -104 - -2 -59 45 -1 -24 35 -10 1 25 16 15 2 21 5 3 -5 4 -15 -25 2nd differences are the same, so we can conclude that we have a quadratic relationship A parabola is a graph of a symmetric quadratic relation

What do they have in common? y = -5x2 + 20x + 1 y = x2 - 50x + 6 y = -2x2 + 2x - 3 y = 4x2 - x - 1 The highest degree is always 2for a quadratic relationship. Which one of these is not a quadratic relationship? a) y = 2x2 + 3 b) y = 4x - 9 c) y = -x2 + x d) y = x2 + 3x + 9 The highest degree in (b) is 1, not 2

In Summary… Graph of a quadratic relation: y = ax2+bx+c, where a≠0 Any relation with a polynomial of degree 2 is quadratic 2nd differences must be constant, not zero When a > 0, parabola opens up When a < 0, parabola opens down Changing b changes location of line of symmetry Constant c is the y-intercept of the parabola