Which equation has a graph that lies entirely above the x-axis? y = –(x + 7)2 + 7 y = (x – 7)2 – 7 y = (x – 7)2 + 7 y = (x – 7)2
Answers
y = –(x + 7)² + 7
Find the x-intercept:
–(x + 7)² + 7 = 0
–(x + 7)² = - 7
(x + 7)² = 7
x + 7 = ±√7
x = ±√7 - 7
There are two points (√7 - 7, 0) and (-√7 - 7, 0) on the x-axis
⇒ The graph cuts the x-axis
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y = (x – 7)² – 7
Find x-intercept:
(x – 7)² – 7 = 0
(x - 7)² = 7
x - 7 = ±√7
x = ±√7 + 7
There are two points (√7 + 7, 0) and (-√7 + 7, 0) on the x-axis
⇒ The graph cuts the x-axis
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y = (x – 7)² + 7
Find the x-intercept:
(x – 7)² + 7 = 0
(x – 7)² = - 7
(x – 7)² = √-7 (imaginary number)
⇒ The graph does not cut the x-axis
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y = (x – 7)²
Find the x-intercept:
(x – 7)² = 0
x - 7 = 0
x = 7
The graph cuts the x-axis at one point, (7 , 0)
⇒ The graph touches the x-axis at one point
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Answer: y = (x – 7)² + 7
