Transforming Parabolas Worksheet
Use vertex form to describe and graph transformed parabolas. Includes a worked example, printable practice, and an answer key with explanations.
The answer key follows the practice below. In the editor, remove the final answer-key section before sharing a student copy.
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Transforming Parabolas
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Learning goal and worked example
Use vertex form to describe and graph transformed parabolas.
For y = 2(x+3)²−1, vertex = (−3,−1), axis = x=−3, and points (−2,1), (−4,1) check the vertical stretch.
Prerequisites: squaring, coordinates, and symmetry. The stretch factor is positive; a negative coefficient also reflects the graph.
Read each question carefully and provide the best answer. Show all your work where applicable.
1. Which transformation shifts the graph of y = x² three units to the right?
y = x² + 3
y = x² - 3
y = (x + 3)²
y = (x - 3)²
2. The graph of y = -2x² is a reflection of y = x² across the x-axis and a vertical stretch by a factor of:
1/2
2
-2
-1/2
3. The vertex form of a parabola is y = a(x - h)² + k, where (h, k) represents the of the parabola.
4. A positive value for 'a' in the equation y = a(x - h)² + k indicates that the parabola opens .
5. Describe the transformations applied to the graph of y = x² to obtain the graph of y = (x + 4)² - 1.
6. A vertical compression by a factor of 1/3 means the 'a' value in y = ax² is 3.
True
False
7. Reflecting a parabola across the y-axis changes the sign of the 'h' value in vertex form.
True
False
8. Graph the parent function y = x² and the transformed function y = -(x - 2)² + 3 on the same coordinate plane. Label both parabolas.
Match the equation with its description of transformation from y = x².
9. y = (x + 5)²
a. Shifted down 2 units
10. y = x² - 2
b. Shifted left 5 units
11. y = 3x²
c. Vertical stretch by factor of 3
12. y = -x²
d. Reflected across the x-axis
Answer key and worked solutions
1. d: y=(x−3)². 2. b: factor 2. 3. Vertex. 4. Upward.
5. Shift left 4 and down 1; vertex (−4,−1).
6. False: a=1/3. 7. True: substituting −x gives a(−x−h)²+k = a(x+h)²+k, moving vertex h to −h.
8. Parent vertex (0,0), points (±1,1),(±2,4). Transformed vertex (2,3), points (1,2),(3,2),(0,−1),(4,−1), opening downward.
Matching: 9 b; 10 a; 11 c; 12 d.
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