3.2 NOTES Graphing Parabolas in Vertex Form LESSON 3.2 - Graphing Parabolas in Vertex Form • Yesterday we learned that parabolas shrink and stretch and they may be reflected in the x‑axis when the value of a changes (given an equation of the form y = ax 2 + bx + c). • If |a| > 1, then the parabola is narrower than the parent function. • If |a| < 1, then the parabola is wider than the parent function. • If a > 1, then the parabola opens up. • If a < 1, then the parabola opens down (it is reflected in the x‑axis). • Today we will explore how to translate the parabola around the plane. Graph the parabola. Compare it to the parent function. y = x 2 +3 x y -2 -1 0 1 2 7 4 3 4 7 The parabola was translated 3 units up. Graph the parabola. Compare it to the parent function. y = x 2 ‑7 x y -2 -1 0 1 2 -3 -6 -7 -6 -3 The parabola was translated 7 units down. Graph the parabola. Compare it to the parent function. y =(x‑ 4) 2 x y -2 -1 0 1 2 36 25 16 9 4 The parabola was translated 4 units to the right. 3 4 5 1 0 1 Graph the parabola. Compare it to the parent function. y =(x + 6) 2 x y -2 -1 -3 -4 -5 16 25 9 4 1 The parabola was translated 6 units to the left. -6 -7 -8 0 1 4
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3.2 NOTES - Graphing Parabolas in Vertex Form · 3.2 NOTES Graphing Parabolas in Vertex Form LESSON 3.2 - Graphing Parabolas in Vertex Form • Yesterday we learned that parabolas
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3.2 NOTES Graphing Parabolas in Vertex Form
LESSON 3.2 - Graphing Parabolas in Vertex Form
• Yesterday we learned that parabolas shrink and stretch and they may be reflected in the x‑axis when the value of a changes (given an equation of the form y = ax2 + bx + c).
• If |a| > 1, then the parabola is narrower than the parent function.
• If |a| < 1, then the parabola is wider than the parent function.
• If a > 1, then the parabola opens up.
• If a < 1, then the parabola opens down (it is reflected in the x‑axis).
• Today we will explore how to translate the parabola around the plane.
Graph the parabola. Compare it to the parent function.
y = x2 + 3x y
-2-1012
74347 The parabola was
translated 3 units up.
Graph the parabola. Compare it to the parent function.
y = x2 ‑ 7x y
-2-1012
-3-6-7-6-3 The parabola was
translated 7 units down.
Graph the parabola. Compare it to the parent function.
y = (x ‑ 4)2x y
-2-1012
36251694 The parabola was translated
4 units to the right.345
101
Graph the parabola. Compare it to the parent function.
y = (x + 6)2x y
-2-1-3-4-5
1625941 The parabola was translated
6 units to the left.-6-7-8
014
3.2 NOTES Graphing Parabolas in Vertex Form
Graph the parabola. Compare it to the parent function.
y = ‑2(x + 1)2 + 5x y
-2-1012
353-313
The parabola was translated 1 unit left and 5 units up. It was also reflected in the x-axis and has a vertical stretch of a = 2.
CHARACTERISTICS OF PARABOLASGiven a parabola in Vertex Form: y = a(x ‑ h)2 + k:
• The parabola opens up if a > 0 and opens down if a < 0
• The parabola is wider than the parent function if |a| < 1
• The parabola is narrower than the parent function if |a| > 1
• The vertex is the point (h, k)
• The axis of symmetry is the vertical line through x = h
Identify the vertex of each parabola.
A) y = (x ‑ 9)2 + 4
B) y = 2(x + 1)2 ‑ 5
C) y = ‑ (x ‑ 3)2 ‑ 8
D) y = ‑(x + 6)2
(9, 4)
(-1, -5)
(3, -8)
(-6, 0)
Identify the vertex of each parabola.
E) y = (x + 8)2 ‑ 3
F) y = ‑ (x ‑ 7)2
G) y = ‑4(x ‑ 10)2 + 2
H) y = 6x2 ‑ 5
(-8, -3)
(7, 0)
(10, 2)
(0, -5)
HOW TO GRAPH PARABOLAS
STEP 1: Find and plot the vertex of the parabola.
STEP 2: Draw the axis of symmetry through that point
STEP 3: Plot a couple more points on one side of the parabola (choose values for x, plug them in to find y)
STEP 4: Use symmetry to plot the mirror‑image of those points on the opposite side of the axis of symmetry
STEP 5: Connect the points to form a U‑shape
Graph the parabola.
y = 3(x + 1)2 ‑ 8x y
-1012
-8-5419
vertex
3.2 NOTES Graphing Parabolas in Vertex Form
Graph the parabola.
y = ‑(x ‑ 4)2 + 3x y
4321
32-1-6
vertex
0 -13
Graph the parabola.
y = (x ‑ 6)2 ‑ 2x y630-3
-211025
vertex
Graph the parabola.
y = ‑ x2 + 7x y
024
72
-13
vertex
HOMEWORK:3.2 Worksheet ‑ Graphing Parabolas in Vertex Form