Answers
This is the same as writing y = sqrt(4(x+5)) - 1
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Explanation:
The given graph appears to be a square root function.
The marked points on the curve are:
(-4,1)(-1,3)(4,5)Reflect those points over the line y = x. This will have us swap the x and y coordinates.
(-4,1) becomes (1,-4)(-1,3) becomes (3,-1)(4,5) becomes (5,4)Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.
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Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).
Plug the coordinates of each point into the template y = ax^2+bx+c.
For instance, plug in x = 1 and y = -4 to get...
y = ax^2+bx+c
-4 = a*1^2+b*1+c
-4 = a+b+c
Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c
Repeat for (5,4) and you should get 4 = 25a+5b+c
We have this system of equations
-4 = a+b+c-1 = 9a+3b+c4 = 25a+5b+cUse substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.
In other words
a = 1/4, b = 1/2, c = -19/4
We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4
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Next we complete the square
y = (1/4)x^2+(1/2)x-19/4
y = (1/4)( x^2+2x )-19/4
y = (1/4)( x^2+2x+0 )-19/4
y = (1/4)( x^2+2x+1-1 )-19/4
y = (1/4)( (x^2+2x+1)-1 )-19/4
y = (1/4)( (x+1)^2-1 )-19/4
y = (1/4)(x+1)^2- 1/4 - 19/4
y = (1/4)(x+1)^2 + (-1-19)/4
y = (1/4)(x+1)^2 - 20/4
y = (1/4)(x+1)^2 - 5
The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.
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The last batch of steps is to find the inverse.
Swap x and y. Then solve for y.
y = (1/4)(x+1)^2 - 5
x = (1/4)(y+1)^2 - 5
x+5 = (1/4)(y+1)^2
(1/4)(y+1)^2 = x+5
(y+1)^2 = 4(x+5)
y+1 = sqrt(4(x+5))
y = sqrt(4(x+5)) - 1
I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.
You can also use a tool like GeoGebra to verify the answer.
Related Questions
60, 69, 79, 80, 86, 86, 86, 89, 90, 100
Which test score is an outlier?
60
69
90
100
Answers
The test score that is an outlier is 60. Option A
What is an outlierA data point that dramatically deviates from the dataset's main pattern or trend is referred to as an outlier.
From the information given, we have that;
The score are;
60, 69, 79, 80, 86, 86, 86, 89, 90, and 100.
We can see that the outlier is 60.
This is due to the fact that all of the other scores, which range from 69 to 100, are considerably higher and closer in value.
The score of 60, however, is considerably lower than the others pupils.
Learn more about outliers at: https://brainly.com/question/3631910
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if Ra radius is 10cm , what will be the diameter and the area of the circle
Answers
Answer:
Diameter=20 cm, Area=100[tex]\pi[/tex]
Step-by-step explanation:
To find the diamter of a circle (given the radius), you multiply the radius by 2. 10cm*2=20 cm. The area of a circle is the radius squared times pi. 10^2 times pi is equal to 100[tex]\pi[/tex].