Assignment red pen highlighter textbook GP notebook graphing
Assignment, red pen, highlighter, textbook, GP notebook, graphing calculator Graph y = (x + 3)2 for – 6 ≤x ≤ 0. Be sure to label your graph completely. x – 6 – 5 – 4 – 3 – 2 – 1 0 y 9 4 1 10 +3 8 parabola 6 2 1 9 y = (x + 3)2 +1 4 0 4 y – 6 – 4 Vertex (– 3, 0) – 2 2 – 2 4 +1 Completely x labeled 6 graph – 4 total:
Part 1: Graph the parabolas using a graphing calculator. Record any observations you notice about the similarities and differences of each parabola with the parent graph, y = x 2. Parent Graph: y = x 2 x y -3 -2 -1 0 9 4 1 0 10 1 1 2 4 3 9 y 8 6 4 2 – 10 – 8 – 6 – 4 – 2 – 4 – 6 – 8 – 10 2 4 6 x 8 10
Parent Graph: y = x 2 10 y = (x – 7)2 y 10 8 6 4 4 2 2 – 10 – 8 – 6 – 4 – 2 2 4 6 x 8 10 – 8 – 6 – 4 – 2 – 4 – 6 – 8 – 10 y 2 4 6 x 8 10 Observations: The graph is shifted right 7 units.
y = (x + 2)2 10 y = (x – 3)2 y 10 8 6 4 4 2 2 – 10 – 8 – 6 – 4 – 2 2 4 6 x 8 10 – 8 – 6 – 4 – 2 – 4 – 6 – 8 – 10 The graph is shifted left 2 units. y 2 4 6 x 8 10 The graph is shifted right 3 units.
2 + k y = a(x – h) The general equation of parabolas is _________. Describe what h does to the equation: left x + h shifts the graph to the ______ right x – h shifts the graph to the ______
WITHOUT using a graphing calculator, graph the following parabolas using the patterns you previous discovered. Be sure to identify the vertex. a) y = (x – 4)2 b) y = (x + 6)2 4 units 6 units Shift the parent graph ___ right (4, 0) left (– 6, 0) ______. Vertex: ________ 10 y 10 8 6 4 4 2 2 – 10 – 8 – 6 – 4 – 2 2 4 6 x 8 10 – 8 – 6 – 4 – 2 – 4 – 6 – 8 – 10 y 2 4 6 x 8 10
WITHOUT using a graphing calculator, graph the following parabolas using the patterns you previous discovered. Be sure to identify the vertex. c) y = (x + 1)2 d) y = (x – 8)2 1 units 8 units Shift the parent graph ___ left (– 1, 0) right (8, 0) ______. Vertex: ________ 10 y 10 8 6 4 4 2 2 – 10 – 8 – 6 – 4 – 2 2 4 6 x 8 10 – 8 – 6 – 4 – 2 – 4 – 6 – 8 – 10 y 2 4 6 x 8 10
Part 2: Graph the parabolas using a graphing calculator. Record any observations you notice about the similarities and differences of each parabola with the parent graph, y = x 2 + 5 The graph is shifted up 5 units. 10 y = x 2 – 9 The graph is shifted down 9 units. y 10 8 6 4 4 2 2 – 10 – 8 – 6 – 4 – 2 2 4 6 x 8 10 – 8 – 6 – 4 – 2 – 4 – 6 – 8 – 10 y 2 4 6 x 8 10
Part 2: Graph the parabolas using a graphing calculator. Record any observations you notice about the similarities and differences of each parabola with the parent graph, y = x 2 – 2 y = (x – 4)2 + 3 The graph is shifted right 4 The graph is shifted units and up 3 units. down 2 units. 10 y 10 8 6 4 4 2 2 – 10 – 8 – 6 – 4 – 2 2 4 6 x 8 10 – 8 – 6 – 4 – 2 – 4 – 6 – 8 – 10 y 2 4 6 x 8 10
Given that the general equation of parabolas is y = a(x – h)2 + k, describe what k does to the equation: up + k shifts the graph ______ down – k shifts the graph ______ Put it together: y = a(x – h)2 + k Shifts the parabola up or down Shifts the parabola left or right
WITHOUT using a graphing calculator, graph the following parabolas. Identify the types of translation and the vertex. a) y = x 2 – 4 b) y = (x + 7)2 0 units Horizontal Shift: ______ down 4 units Vertical Shift: _______ left 7 units Horizontal Shift: ______ 0 units Vertical Shift: _______ (0, – 4) Vertex: _______ (– 7, 0) Vertex: _______ 10 y 10 8 6 4 4 2 2 – 10 – 8 – 6 – 4 – 2 2 4 6 x 8 10 – 8 – 6 – 4 – 2 – 4 – 6 – 8 – 10 y 2 4 6 x 8 10
WITHOUT using a graphing calculator, graph the following parabolas. Identify the types of translation and the vertex. c) y = (x – 1)2 – 9 right 1 units Horizontal Shift: ______ down 9 units Vertical Shift: _______ (1, – 9) Vertex: _______ 10 d) y = (x + 2)2 – 3 left 2 units Horizontal Shift: ______ down 3 units Vertical Shift: _______ (– 2, – 3) Vertex: _______ y 10 8 6 4 4 2 2 – 10 – 8 – 6 – 4 – 2 2 4 6 x 8 10 – 8 – 6 – 4 – 2 – 4 – 6 – 8 – 10 y 2 4 6 x 8 10
OLD SLIDES
Investigate a Parabola PG – 5 a) Draw the graph of y = (x – 2)2. Since we are going to do this by hand, be sure to use the domain – 1 ≤ x ≤ 5. x – 1 0 1 2 3 4 5 10 y 9 8 4 1 6 4 0 9 y = (x – 2)2 2 1 4 y – 6 – 4 – 2 2 – 4 4 6 x Vertex (2, 0)
Investigate a Parabola PG – 5 b) How is this graph different from the graph of y = x 2? What difference in the equation accounts for the difference in graphs? x – 3 – 2 – 1 0 1 2 3 y= 9 4 1 x 2 10 The graph of y = (x – 2)2 is shifted 2 units to the right. 8 y = x 2 6 4 0 1 4 9 y The “ 2” makes the graph shift over. – 6 2 – 4 – 2 y = (x – 2)2 2 – 4 4 6 x
PG – 5 Investigate a Parabola b) Based on your observations in part (b), write an equation with a graph that “sits on” the x–axis at the point (5, 0). 10 y = (x – 5)2 y 8 y = x 2 6 4 2 – 6 – 4 – 2 y = (x – 2)2 2 – 4 4 6 x
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