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Scrat [10]
3 years ago
6

the vertex of this parabola is at (4, -3) when the x-value is 5, the y-value is -6. what is the coefficient of the squared term

in the parabola's equation
Mathematics
1 answer:
Doss [256]3 years ago
5 0
+ The vertex of this parabola is at (4, -3), that means we have the equation of this parabola: y=a(x-4)² -3

+ <span>when the x-value is 5, the y-value is -6, we have  -6=a(5-4)</span>² -3
or we have a= -6+3, and we have a= -3

+ <span>what is the coefficient of the squared term in the parabola's equation, that is a, and a= -3</span>
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hodyreva [135]

Answer:

b) -5x^3+7x^2-15x+75

Step-by-step explanation:

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3 years ago
Write an exponential function that includes the following given pair of points.
alina1380 [7]

Answer:

f(x)=-2^x

Step-by-step explanation:


So generally an exponential equation is expressed in the form: f(x)=a(b)^x and: b=1+r\text{ or }b=1-r \text{ depending on whether it's decaying or growing}. In this case we see that as x increased by 1, the y-decreases, BUT the absolute value is increasing, so it's really just reflected.

Plug in known values:

-2=a(b)^1

-4=a(b)^2

So if you think about it. you really have

-2 = a * b

-4 = a * b * b

since ab = -2, then we can substitute this into the second equation

-4 = -2 * b

-4 = -2b

Divide both sides by -2

b = 2

You can also deduce that b=2, by realizing to go from -2 to -4, you have to subtract 100% of -2 from -2. This means r=1, so b=1+1, b=2

Anyways, now it's time to solve for a, by plugging in a point as well as b.

-4 = a(2)^2

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-1 = a

You can verify this by using the other point

-2 = -(2)^1

-2 = -(2)

-2 = -2

So the equation is: f(x)=-2^x

5 0
2 years ago
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