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pentagon [3]
3 years ago
5

Find allgebraiclly the equation of the axis of symmetry and the vertex of the parabola represented by the equation y=-x2-2x+1

Mathematics
2 answers:
Slav-nsk [51]3 years ago
7 0
To find the vertex use -b/2a (for the x value which is also the axis of symmetry)
So 2/-2 = -1 Therefore the axis of symmetry is x=-1 Plug in for the y value:
y= -(-1)^2 -2(-1) + 1 y=-1 + 2 + 1 y=2 Vertex (-1,2)
vova2212 [387]3 years ago
6 0
The vertex can be found by finding when the derivative is equal to zero (velocity is zero)

dy/dx=-2x-2

dy/dx=0 when -2x-2=0, -2x=2, x=-1

y(-1)=-(-1^2)-2(-1)+1

y(-1)=-1+2+1=2

So the vertex is at the point (-1,2) and the axis of symmetry is the line:

x=-1
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3(x-4) = x + 14<br> How do you solve this equation
Dmitry_Shevchenko [17]

Answer:

x=13

Step-by-step explanation:

you have to isolate the variable

3(x-4)=x+14

distribute

3x-12=x+14

subtract 14 from each side

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subtract 3x from each side

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divide each side by -2

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hope this helps!!! :)

4 0
3 years ago
Read 2 more answers
A $16,000 robot depreciates linearly to zero in 10 years. (a) find a formula for its value as a function of time, t, in years.
SVETLANKA909090 [29]

We are given, cost of the robot for 0 number of year = $16,000.

0 represents initial time of the robot.

After 10 year cost of the robot is = $0

The problem is about the number of the years and cost of the robot over different number of years.

So, we could take x coordinate by number of hours and y coordinate for y number of hours.

So, from the problem, we could make two coordinates for the given situation.

(x1,y1) = (0, 16000) and (x2,y2) = (10, 0).

In order to find the function of time, we need to find the rate at which robot rate depreciates each year.

Slope is the rate of change.

So, we need to find the slope of the two coordinates we wrote above.

We know, slope formula

Slope (m) = \frac{y2-y1}{x2-x1}

Plugging values in formula, we get

m=\frac{0-16000}{10-0} = \frac{-16000}{-10} = -1600.

Brecasue of depreciation we got a negative number for slope or rate of change.

Therefore, rate of depreciation is $1600 per year.

We already given inital cost, that is $16,000.

So, we can setup an a function

f(x) = -1600x + 16000.

But the problem is asked to take the variable t for time.

Replacing x by t, we get

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8 0
3 years ago
Y&gt;1 and y&gt;x on a graph
zlopas [31]

So,

y>1\wedge y>x

1. Graph each inequality separately.

2. Choose a test point to determine which side of the line needs to be shaded.

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As for the system of inequalities we say it's unbounded.

3 0
3 years ago
Triangle GCH is similar to triangle DCE. Find CH
soldier1979 [14.2K]

Answer:

x = 65

Step-by-step explanation:

if two triangles are similar then we can use the similarity ratio to find the length of CH

60/156 = x/169 cross multiply expressions

156x = 10140 divide both sides by 156

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3 years ago
Can someone help me .
insens350 [35]
Y-y1=m(x-x1)
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7 0
3 years ago
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