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ruslelena [56]
4 years ago
13

If f(x) = x^2 is reflected over the x-axis and the shifted 4 units down, what is the equation of the new function, g(x)?

Mathematics
1 answer:
NARA [144]4 years ago
6 0

Answer:

g(x) = -x² - 4

Step-by-step explanation:

In this case, we are only changing <em>a </em>(reflection and vertical shrink/stretch) and <em>k </em>(vertical movement)

<em>k </em>= -4 because we are moving 4 units down

<em>a </em>= -1 because we are just reflecting over the x-axis

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tensa zangetsu [6.8K]
If the parabola has y = -4 at both x = 2 and x = 3, then since a parabola is symmetric, its axis of symmetry must be between x = 2 and x = 3, or at x = 5/2. Our general equation can then be:
y = a(x - 5/2)^2 + k
Substitute (1, -2): -2 = a(-3/2)^2 + k
-2 = 9a/4 + k
Substitute (2, -4): -4 = a(-1/2)^2 + k
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Subtracting: 2 = 2a, so a = 1. Substituting back gives k = -17/4.
So the equation is y = (x - 5/2)^2 - 17/4
Expanding: y = x^2 - 5x + 25/4 - 17/4
y = x^2 - 5x + 2 (This is the standard form.)
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Will give Brainliest!!!
castortr0y [4]

Answer:

a

Step-by-step explanation:

if you plug 4 in for x it solves it

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Step-by-step explanation:

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