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fgiga [73]
3 years ago
14

Select the graph that correctly represents ƒ(x) = –2(x + 4)2 – 1.Find the equation of the parabola with its focus at (3,4) and i

ts directrix y = 0.
Mathematics
1 answer:
IgorC [24]3 years ago
3 0

Answer:

Equation of parabola:  8*(y - 2) = (x - 3)^2

or

y = (1/8)*(x - 3)^2 + 2

Step-by-step explanation:

focus at (3,4) and its directrix y = 0.

Focus equation:  (h, k + c) = (3, 4)

Directrix equation  y =  k - c = 0

so  h = 3,   k + c = 4,   k - c = 0

Solve  the system :  k + c = 4 and k - c = 0

add the equations together:     k + c + k - c = 4 + 0

2k = 4

k = 2

so   k + c = 4,    2 + c = 4,   c = 2

4c (y - k) = (x -  h)^2

4*2 *(y - 2) = (x - 3)^2

8*(y - 2) = (x - 3)^2

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Answer:

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Step-by-step explanation:

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What is the area of a garden that measures 4mx4mx6mx4mx10mx8m
topjm [15]

The area of the garden is 120 square metre

<h2>Explanation:</h2>

The picture of the garden is shown below. In this problem, we have:

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Recall that the area of a square is given by:

A_{s}=L^2 \\ \\ A_{s}:Area \ of \ a \ square \\ L:Side \ of \ the \ square

On the other hand, the area of a rectangle is given by:

A_{r}=L_{1}\times L_{2} \\ \\ \\ A_{r}:Area \ of \ a \ rectangle \\ \\ L_{1}:Side \ 1 \ of \ the \ rectangle \\ \\ L_{2}:Side \ 2 \ of \ the \ rectangle

Therefore:

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L=4m \\ \\ \\ Substituting \ values: \\ \\ \\ A_{s}=4^2 \\ \\ \boxed{A_{s}=16m^2}

FOR THE RECTANGLE 1:

L_{1}=6m \\ L_{2}=4m \\ \\ \\ Substituting \ values: \\ \\ \\ A_{r_{1}}=6(4) \\ \\ \boxed{A_{r_{1}}=24m^2}

FOR THE RECTANGLE 2:

L_{1}=10m \\ L_{2}=8m \\ \\ \\ Substituting \ values: \\ \\ \\ A_{r_{2}}=10(8) \\ \\ \boxed{A_{r_{2}}=80m^2}

Finally, the area of a garden is the sum of the three areas:

A_{total}=A_{s}+A_{r_{1}}+A_{r_{2}} \\ \\ A_{total}=16m^2+24m^2+80m^2 \\ \\ A_{total}=16+24+80 \\ \\ \boxed{A_{total}=120m^2}

<h2>Learn more:</h2>

Area of a pizza: brainly.com/question/12878495

#LearnWithBrainly

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Step-by-step explanation:

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