Finding Extrema Common Core II – Day 4

Warm-Up #1 Find coordinates of x-intercepts, y-intercept, and Vertex. Is the vertex a maximum or minimum? 1. f(x) = -x (7 – x) 2. f(x) = -2(x – 3)(x – 8) 3. x (7 – x)

HW Check

Review x-intercepts at (-2, 0) and (6, 0) with graph opening upward Write rules for quadratic functions with graphs that meet these conditions: x-intercepts at (-2, 0) and (6, 0) with graph opening upward x-intercepts at (2, 0) and (6, 0) with graph opening downward 1. y=(x+2)(x-6) 2. y = -1(x – 2)(x – 6)

Write a quadratic to match these conditions: 3) x-intercepts at (2, 0) and (6, 0) f(x) = (x – 2)(x – 6) What is the vertex of this quadratic? (4, -4) What could we multiply the “y” value of the vertex “-4” by so that the minimum becomes (4, -8)? Final quadratic becomes: f(x) = 2(x – 2)(x – 6)

Write the quadratic to match these conditions: 4. x-intercepts at (-2, 0) and (4, 0) with a minimum at (1, -3) 5. X-intercepts at (-9, 0) and (3, 0) with a maximum at (-3, 6) 6. x-intercepts at (-2, 0) and (2, 0) with a maximum at (0, 8) 4. (x + 2) (x – 4) * (1/3) 5. (x +9) (x – 3) *( - 1/6) 6. (x + 2) (x – 2)*(-2)

Write the quadratic to match these conditions 7. x-intercepts at (-2, 0) and (6, 0) f(x) = (x + 2)(x – 6) What is the y-intercept of this quadratic? “c” value which is -12 What could we multiply “c” (-12) by in order to change the y-intercept to (0, -60) 5 The quadratic with x-intercepts at (-2, 0) and (6, 0) with y-intercept at (0, -60) f(x) = 5(x + 2)( x – 6)

8. x-intercepts at (-3, 0) and (3, 0) and a y-intercept at (0, 9) 9 8. x-intercepts at (-3, 0) and (3, 0) and a y-intercept at (0, 9) 9. x-intercepts at (-3, 0) and (1, 0) and a y-intercept at (0, -6) 10. x-intercepts at (-5, 0) and (-3, 0) and a y-intercept at (0, 3) 8. Y = (x + 3) (x -3) *-1 9. Y = 2(x+3)(x-1) 10. Y = (1/5)(x + 5)(x +3)

Complete a, d, e, f, g, h

Homework Quadratic worksheet. Finding extrema day 2.

Extra Practice

Let’s Play some Musical Chairs! There are 5 stations around the classroom with a quadratic equation When I say go, you have 30 seconds to take your worksheet and pencil and move to one station Once everyone is at a station, the music will begin playing and you will need to spend the duration of the song trying to find the important key points When the music stops, you must stop writing immediately and go to the next station When we are finished with 5 songs, you will be given the opportunity to finish your graphs with one last song