Completely labeled graph Assignment, red pen, highlighter, textbook, GP notebook, graphing calculator U4D1 Have out: Bellwork: Graph y = (x + 3)2 for –6 ≤x ≤0. Be sure to label your graph completely. y x 2 4 6 –2 –4 –6 8 10 x y –6 –5 –4 –3 –2 –1 9 +3 4 y = (x + 3)2 +1 parabola 1 +1 1 Completely labeled graph 4 9 Vertex (–3, 0) total:

Take out the Translate Parabolas worksheet 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 = x2. x y 4 6 8 10 2 –2 –4 –6 –8 –10 Parent Graph: y = x2 x -3 -2 -1 1 2 3 y 9 4 1 1 4 9

The graph is shifted right 7 units. Parent Graph: y = x2 y = (x – 7)2 x y 4 6 8 10 2 –2 –4 –6 –8 –10 x y 4 6 8 10 2 –2 –4 –6 –8 –10 Observations: The graph is shifted right 7 units.

The graph is shifted left 2 units. The graph is shifted right 3 units. y = (x + 2)2 y = (x – 3)2 x y 4 6 8 10 2 –2 –4 –6 –8 –10 x y 4 6 8 10 2 –2 –4 –6 –8 –10 The graph is shifted left 2 units. The graph is shifted right 3 units.

Conclusions: y = a(x – h)2 + k x + h left x – h right The general equation of parabolas is _________________. Describe what h does to the equation: x + h left ______ shifts the graph to the ________. x – h right ______ 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. Practice #1: a) y = (x – 4)2 b) y = (x + 6)2 Shift the parent graph ___ units ______. Vertex: ________ 4 Shift the parent graph ___ units ______. Vertex: ________ 6 right (4, 0) left (–6, 0) x y 4 6 8 10 2 –2 –4 –6 –8 –10 x y 4 6 8 10 2 –2 –4 –6 –8 –10

WITHOUT using a graphing calculator, graph the following parabolas using the patterns you previous discovered. Be sure to identify the vertex. Practice: c) y = (x + 1)2 d) y = (x – 8)2 Shift the parent graph ___ units ______. Vertex: ________ 1 Shift the parent graph ___ units ______. Vertex: ________ 8 left (–1, 0) right (8, 0) x y 4 6 8 10 2 –2 –4 –6 –8 –10 x y 4 6 8 10 2 –2 –4 –6 –8 –10

The graph is shifted up 5 units. The graph is shifted down 9 units. 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 = x2. y = x2 + 5 y = x2 – 9 The graph is shifted up 5 units. The graph is shifted down 9 units. x y 4 6 8 10 2 –2 –4 –6 –8 –10 x y 4 6 8 10 2 –2 –4 –6 –8 –10

The graph is shifted down 2 units. 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 = x2. y = x2 – 2 y = (x – 4)2 + 3 The graph is shifted down 2 units. The graph is shifted right 4 units and up 3 units. x y 4 6 8 10 2 –2 –4 –6 –8 –10 x y 4 6 8 10 2 –2 –4 –6 –8 –10

Conclusions: + k up – k down y = a(x – h)2 + k Given that the general equation of parabolas is y = a(x – h)2 + k, describe what k does to the equation: + k up ______ shifts the graph ________. – k down ______ shifts the graph ________. Put it together: y = a(x – h)2 + k Shifts the parabola up or down Shifts the parabola left or right

Practice #2: a) y = x2 – 4 b) y = (x + 7)2 0 units left 7 units WITHOUT using a graphing calculator, graph the following parabolas. Identify the types of translation and the vertex. Practice #2: a) y = x2 – 4 b) y = (x + 7)2 0 units left 7 units Horizontal Shift: ___________ Horizontal Shift: ___________ down 4 units 0 units Vertical Shift: _____________ Vertical Shift: _____________ (0, –4) (–7, 0) Vertex: _______ Vertex: _______ x y 4 6 8 10 2 –2 –4 –6 –8 –10 x y 4 6 8 10 2 –2 –4 –6 –8 –10

Practice #2: c) y = (x – 1)2 – 9 d) y = (x + 2)2 – 3 right 1 units WITHOUT using a graphing calculator, graph the following parabolas. Identify the types of translation and the vertex. Practice #2: c) y = (x – 1)2 – 9 d) y = (x + 2)2 – 3 right 1 units left 2 units Horizontal Shift: ___________ Horizontal Shift: ___________ down 9 units down 3 units Vertical Shift: _____________ Vertical Shift: _____________ (1, –9) (–2, –3) Vertex: _______ Vertex: _______ x y 4 6 8 10 2 –2 –4 –6 –8 –10 x y 4 6 8 10 2 –2 –4 –6 –8 –10

Finish today's assignment: worksheet & PG 15 - 20

OLD SLIDES

Let's look at PG - 5 from yesterday's assignment.

Investigate a Parabola PG – 5 Investigate a Parabola 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. y x 2 4 6 –2 –4 –6 8 10 x y –1 1 2 3 4 5 9 4 1 y = (x – 2)2 1 4 9 Vertex (2, 0)

Investigate a Parabola PG – 5 Investigate a Parabola b) How is this graph different from the graph of y = x2? What difference in the equation accounts for the difference in graphs? y x 2 4 6 –2 –4 –6 8 10 x y = x2 –3 –2 –1 1 2 3 The graph of y = (x – 2)2 is shifted 2 units to the right. 9 y = x2 4 1 The “2” makes the graph shift over. 1 y = (x – 2)2 4 9

Investigate a Parabola 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). y x 2 4 6 –2 –4 –6 8 10 y = (x – 5)2 y = x2 y = (x – 2)2