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4 years ago

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

Mathematics

1 answer:

omeli [17]4 years ago

3 0

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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Step-by-step explanation:

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3 years ago

Find the distance between the points t(13, 1.6)t(13, 1.6) and v(5.4, 3.7)v(5.4, 3.7).

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The distance between any 2 points P(a,b) and Q(c,d) in the coordinate plane, is given by the formula:

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}$

Thus the distance between points t(13, 1.6) and v(5.4, 3.7) is found using the formula as:

$|tv|= \sqrt{(13-5.4)^{2} + (1.6-3.7)^{2}}= \sqrt{ (7.6)^{2}+ (-2.1)^{2}}=\\\\ \sqrt{57.76+4.41}= \sqrt{62.17} \approx 7.9$

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3 years ago