Answer: g(x) = (x-2)^2 + 1. Choice C
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Explanation:
The graphs have the same shape, which means they have the same 'a' value.
In this case, a = 1.
The vertex of the red graph is (0,0).
The vertex of the blue parabola is (2, 1)
The red curve has been shifted 2 units to the right and 1 unit up.
Since the vertex of the blue graph is (2,1), this means h = 2 and k = 1.
Plug a = 1, h = 2 and k = 1 to get...
y = a(x-h)^2 + k
y = 1(x-2)^2 + 1
g(x) = (x-2)^2 + 1
Answer:
(- 2, 4 )
Step-by-step explanation:
y = 2x + 8 → (1)
y = - 2x → (2)
substitute y = 2x + 8 into (2)
2x + 8 = - 2x ( add 2x to both sides )
4x + 8 = 0 ( subtract 8 from both sides )
4x = - 8 ( divide both sides by 4 )
x = - 2
substitute x = - 2 into (2)
y = - 2(- 2) = 4
solution is (- 2, 4 )
Based on the calculations, the equation of this parabola is equal to (x - 6)² = 16(y + 4).
<h3>How to determine the equation of this parabola?</h3>
Mathematically, the standard equation with the vertex for a parabola is given by:
(y - k)² = 4a(x - h) for horizontal parabola.
(x - h)² = 4a(y - k) for vertical parabola.
<u>where:</u>
By critically observing the points, we can deduce that both the focus and vertex lie on the same vertical line x = 6.
<u>Given the following data:</u>
Focus with points = (6, 2).
Vertex (h, k) = (6, –4).
<u>Note:</u> a = 2 - (-4) = 2 + 4 = 6.
Substituting the given parameters into the formula, we have;
(x - 6)² = 4 × 4(y - (-4))
(x - 6)² = 16(y + 4).
Read more on parabola here: brainly.com/question/2346582
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Answer:
48 quarts = 12 gallons
Step-by-step explanation:
