5 Complete the SquareExample: Given f(x) = 2x2 - 8x + 1, complete the square to put it into the form f(x) = a(x – h)2 + k.How about f(x) = x2 - 3x + 1?
6 The Graph of a Quadratic Maximum pointVertexyyxxMinimum pointVertexAxis of symmetryx = hAxis of symmetryx = h
7 Find vertex of a parabola Transformation form: f(x) = a(x – h)2 + kVertex : ( h, k ) Axis of symmetry: x = hTransformation form: f(x) = ax2 + bx + cVertex : ( - b/2a, f(- b/2a) ) Axis of symmetry: x = -b/2a
8 Graphing parabolas Determine if the graph opens up or down Determine the vertex ( h, k )Find the y – interceptPlot the vertex and at least 2 additional points on one side of the vertexUse symmetry finish the other halfExample: f(x) = 2x2 + x - 3
9 Application f(x) = a ( x – h )2 + k 5 10 8 3 Write the equation of the parabola with vertex at (8, 3) passing through (10, 5).f(x) = a ( x – h )2 + k51083
10 Height of a Projected Object If air resistance is neglected, the height s ( in feet ) of an object projected directly upward from an initial height s0 feet with initial velocity v0 feet per second iss (t) = -16t2 + v0t + s0,where t is the number of seconds after the object is projected.
11 ApplicationA ball is thrown directly upward from an initial height of 100 feet with an initial velocity of 80 feet per second.Give the function that describes the height of the ball in terms of time t.Graph this function so that the y-intercept, the positive x- intercept, and the vertex are visible.If the point (4.8, ) lies on the graph of the function. What does this mean for this particular situation?After how many seconds does the projectile reach its maximum height? What is the maximum height? Solve analytically and graphically.For what interval of time is the height of the ball greater than 160 feet? Determine the answer graphically.After how many seconds will the ball fall to the ground? Determine the answer graphically.