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The equation of the new parabola is y = (x - 5)² - 6
Step-by-step explanation:
Let us revise the translation of a function
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k
∵ The equation of the parabola is y = x²
∵ The parabola is shifted down by 6 units
- That means new y = y - k and k = 6
∴ The new y = x² - 6
∵ The parabola is shifted 5 units to the right
- That means the new y = (x - h)² and h = 5
∴ The new y = (x - 5)²
∴ The new equation is y = (x - 5)² - 6
The equation of the new parabola is y = (x - 5)² - 6
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You can learn more about transformation in brainly.com/question/9381523
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