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Crazy boy [7]
3 years ago
8

If f(x) = x2 and g(x) =1/ 2x+3, find g(f(-1)).

Mathematics
1 answer:
Dvinal [7]3 years ago
5 0
-1=1/2x+3
2=1/2x
(2)2=1/2x(2)
4=x
Answer: x=4
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Express each of the following quadratic functions in the form of f(x) = a (x - h)²+ k.Then,state the minimum or maximum value,ax
Ivan

Given:

The function is:

f(x)=-2x^2+7x+4

To find:

Express the quadratic equation in the form of f(x)=a(x-h)^2+k, then state the minimum or maximum value,axis of symmetry and minimum or maximum point.

Solution:

The vertex form of a quadratic function is:

f(x)=a(x-h)^2+k              ...(i)

Where, a is a constant, (h,k) is the vertex and x=h is the axis of symmetry.

We have,

f(x)=-2x^2+7x+4

It can be written as:

f(x)=-2\left(x^2-3.5x\right)+4

Adding and subtracting square of half of coefficient of x inside the parenthesis, we get

f(x)=-2\left(x^2-3.5x+(\dfrac{3.5}{2})^2-(\dfrac{3.5}{2})^2\right)+4

f(x)=-2\left(x^2-3.5x+(1.75)^2\right)-2\left(-(1.75)^2\right)+4

f(x)=-2\left(x-1.75\right)^2+2(3.0625)+4

f(x)=-2\left(x-1.75\right)^2+6.125+4

f(x)=-2\left(x-1.75\right)^2+10.125                ...(ii)

On comparing (i) and (ii), we get

a=-2,h=1.75,k=10.125

Here, a is negative, the given function represents a downward parabola and its vertex is the point of maxima.

Maximum value = 10.125

Axis of symmetry : x=1.75

Maximum point = (1.75,10.125)

Therefore, the vertex form of the given function is f(x)=-2\left(x-1.75\right)^2+10.125, the maximum value is 10.125, the axis of symmetry is x=1.75 and the maximum point is (1.75,10.125).

8 0
3 years ago
What is the answer to the equation 4a+26-9a-17=26?
podryga [215]
First you have to put all of your common numbers together. 4a and 9a go together. You then subtract those because 9 is negative (-9). Then you get -5a. Now move on to your other numbers. You have 26 and 17. 17 is negative as well (-17), so you subtract it from 26. That gives you 9.
Your new equation is -5a + 9 = 26
Now you subtract 9 from both sides. Your positive (+9) will cancel out with your negative (-9). Then subtract it from 26. 9 minus 26 is 17. 
Now your equation is -5a = 17
Since it's negative, you're going to add it (5) to both sides. 
Your 5's cancel out, and 17 + 5 is 22. 
a = 22
22 is the answer 

5 0
3 years ago
Diameter=14.6 <br> round to nearest tenth
grandymaker [24]

The next greater tenth is  14.7
The next smaller tenth is  14.5

Neither of them is nearer to 14.6 than 14.6 already is.
So 14.6 is already the nearest tenth.


4 0
3 years ago
Read 2 more answers
Twenty-five percent of what number is 80?
tankabanditka [31]
The answer is 20
Hope this helps
3 0
2 years ago
Read 2 more answers
Look at the image for the question.
PtichkaEL [24]
I don’t see any images
8 0
3 years ago
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