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bekas [8.4K]
3 years ago
5

F(x)=-1/2(x-2)^2-4 Graph the function

Mathematics
1 answer:
telo118 [61]3 years ago
6 0

Answer:

  see below

Step-by-step explanation:

The function is written in vertex form. It has a negative vertical scale factor, so you know ...

  • the vertex is (2, -4)
  • the vertical scale factor is 1/2
  • the parabola opens downward

Vertex form is ...

  f(x) = a(x -h)^2 +k . . . . . . . . . . vertical scale factor "a", vertex (h, k)

__

Since you know the vertex and scale factor, you can plot some points on the graph. I find it convenient to think in terms of units either side of the vertex. These are values of x that would make (x-2)^2 be 1^2, 2^2, 3^2, 4^2 and so on. The vertical scale factor of -1/2 tells you that the y-differences for these points will be -1/2, -4/2, -9/2, -16/2 from the vertex. Then we have ...

  vertex: (2, -4)

  1 unit either side of the vertex: (1, -4.5), (3, -4.5)

  2 units either side of the vertex: (0, -6), (4, -6)

  3 units either side of the vertex: (-1, -8.5), (5, -8.5)

  4 units either side of the vertex: (-2, -12), (6, -12)

You can plot these points and draw a smooth curve through them. Or, you can let a graphing calculator do it. The result will be similar to that shown below.

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I need help on all 3 of these questions
Jobisdone [24]
1) C is because it’s exactly double the size in both width and length while the others are only gaining one or the other. For example - the a length of the squares is 5 and the length on c is 10, the base on a is 3 long, the base on c is 6. The width on a is 1 and the width on c is 2. You can put these into fractions 5/10 3/6 1/2 but they all equal 1/2. So it’s double the size of a.

5 0
3 years ago
Which of the following could be the perimeter of a rectangle with an area of 24 square inches?
Veronika [31]

Answer: C. 20 inches

Step-by-step explanation:

perimeter= 2 x (4+6)=20 inches

7 0
2 years ago
An object is dropped from a bridge and allowed to freefall to the ground. The height of the object over time can be modeled usin
kkurt [141]

Answer:

<em>t = 3 seconds</em>

Step-by-step explanation:

We have the equation, as a function of time, that describes the height of the object that is dropped from the bridge.

The equation is:

h (t) = 144 - 16t ^ 2

Where t is the time in seconds and h is the height in feet.

To know how long it takes the object to fall to the ground we do h (t) = 0 and solve for t.

So:

0 = 144 - 16t ^ 2\\\\16t ^ 2 = 144\\\\t ^ 2 = \frac{144}{16}\\\\t ^ 2 = 9\\\\t_1 = 3\\t_2 = -3

We take the positive solution.

Therefore the object takes 3 seconds to reach the ground

4 0
3 years ago
Read 2 more answers
the square below is dilated by a scale factor of 1/2. find the perimeter and area of the square below, as well as the perimeter
mars1129 [50]

Answer:

w4

Step-by-step explanation:

3 0
2 years ago
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50 POINTS TO WHOEVER HELPS WITH THIS I NEED IT ASAP PLEASE HELP
Tresset [83]

Answer:

<em>4a ) Difference ⇒ $ 63.24,</em>

<em>4b ) 4 children</em>

Step-by-step explanation:

4a ) If the number of children is represented by the value of x, let us substitute a family of 2 children as value of x into this equation we are given;

y = 21.08 * ( 2 ) + 85.15 ⇒ Multiply 21.08 by 2,

y = 42.16 + 85.15 ⇒ Combine like terms,

y = 127.31

If y ⇒ amount spent on grocery's, let us solve for the amount spent on 5 children, and subtract from this amount;

y = 21.08 * ( 5 ) + 85.15 ⇒ Multiply 21.08 by 5,

y = 105.4 + 85.15 ⇒ Combine like terms,

y = 190.55

Difference; 190.55 - 127.31 = 63.24,

<em>Solution; Difference ⇒ $ 63.24</em>

4b ) If the amount is $ 169.47, let us plug it into our given equation provided amount spent on groceries ⇒ y;

169.47 = 21.08x + 85.15 ⇒ Subtract 85.15 from either side of equation,

21.08x = 84.32 ⇒ Divide either side 21.08,

x = 4 children

<em>Solution; 4 children</em>

7 0
3 years ago
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