Question

The parabola y = x2is shifted down by 6 units and to the right by 5 units.

Answer 1

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

Learn more

You can learn more about transformation in brainly.com/question/9381523

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