Graph the following function and identify any shifts, stretches, and symmetry and x and y intercepts:

y = f (x) = (x - 3) ^2 + 2

Question

Mathematics

Steve Livingston

14 May, 12:38

Graph the following function and identify any shifts, stretches, and symmetry and x and y intercepts:

y = f (x) = (x - 3) ^2 + 2

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Answers (1)

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Douglas Dudley · Answer 1

Step-by-step explanation:

The parent function here is y = x^2, whose graph is that of a parabola that opens up and has its vertex at the origin, (0, 0).

Translating this parent graph 3 units to the right and then up by 2 units will produce the desired graph of y = f (x) = (x - 3) ^2 + 2.

There are no stretches or symmetry.

y-intercept: let x = 0 and find y: 9 + 2 = 11. y-intercept is (0, 11).

x-intercept: let y = 0 and find x: (x - 3) ^2 + 2 = 0 = > (x - 3) ^2 = - 2. This has no real roots. Thus, there are no x-intercepts.

Graph the following function and identify any shifts, stretches, and symmetry and x and y intercepts:y = f (x) = (x - 3) ^2 + 2

Graph the following function and identify any shifts, stretches, and symmetry and x and y intercepts:

y = f (x) = (x - 3) ^2 + 2