1. Algebra: Completing the square 7
Silent
Teacher
Intelligent Practice
Narration
Your Turn
Find the coordinates of the turning point of the graph
𝑦= 2𝑥 2 −4𝑥+1
Find the coordinates of the turning point of the graph
𝑦= 2𝑥 2 −4𝑥+1
Example
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2. Find the coordinates of the turning point of the graph 𝑦= 𝑥 2 −2𝑥+3
Worked Example
Your Turn
Find the coordinates of the
turning point of the graph
𝑦= 𝑥 2 −2𝑥+3
Find the coordinates of the
turning point of the graph
𝑦= 𝑥 2 −2𝑥+6
Find the coordinates of the
turning point of the graph
𝑦= 2𝑥 2 −2𝑥+3
Find the coordinates of the
turning point of the graph
𝑦= 𝑥 2 −2𝑥+6
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3. Find the coordinates of the turning point of the following graphs:
𝑦= 𝑥 2 +10𝑥+4
𝑦=2𝑥 2 +4𝑥+4
𝑦= 𝑥 2 +10𝑥+3
𝑦=2𝑥 2 +4𝑥+3
𝑦= 𝑥 2 +10𝑥+2
𝑦=2𝑥 2 +4𝑥+2
𝑦= 𝑥 2 +10𝑥+1
𝑦=2𝑥 2 +4𝑥+1
𝑦= 𝑥 2 −10𝑥−1
𝑦=2𝑥 2 −4𝑥−1
𝑦= 𝑥 2 −10𝑥−2
𝑦=2𝑥 2 −4𝑥−2
𝑦=𝑥 2 −10𝑥−3
𝑦=2𝑥 2 −4𝑥−3
𝑦=𝑥 2 −10𝑥−4
𝑦=2𝑥 2 −4𝑥−4
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4. Find the coordinates of the turning point of the following graphs:
𝑦= 𝑥 2 +10𝑥+4
(−5,−21)
𝑦=2𝑥 2 +4𝑥+4
(−1,2)
𝑦= 𝑥 2 +10𝑥+3
(−5,−22)
𝑦=2𝑥 2 +4𝑥+3
(−1,1)
𝑦= 𝑥 2 +10𝑥+2
(−5,−23)
𝑦=2𝑥 2 +4𝑥+2
(−1,0)
𝑦= 𝑥 2 +10𝑥+1
(−5,−24)
𝑦=2𝑥 2 +4𝑥+1
(−1,−1)
𝑦= 𝑥 2 −10𝑥−1
(5,−26)
𝑦=2𝑥 2 −4𝑥−1
(1,−3)
(5,−27)
(1,−4)
𝑦= 𝑥 2 −10𝑥−2
𝑦=2𝑥 2 −4𝑥−2
(5,−28)
𝑦=𝑥 2 −10𝑥−3
(1,−5)
𝑦=2𝑥 2 −4𝑥−3
(5,−29)
𝑦=𝑥 2 −10𝑥−4
(1,−6)
𝑦=2𝑥 2 −4𝑥−4
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