SOLUTION: 4. Describe the transformations applied to f(x)=x2 to produce the function f(x)=2(x-5)2+10 5. Convert the following equation into vertex form by completing the square. f(

Algebra ->  Equations -> SOLUTION: 4. Describe the transformations applied to f(x)=x2 to produce the function f(x)=2(x-5)2+10 5. Convert the following equation into vertex form by completing the square. f(      Log On


   

Question 1198841: 4. Describe the transformations applied to f(x)=x2 to produce the function f(x)=2(x-5)2+10

5. Convert the following equation into vertex form by completing the square.
f(x) = 2x2+12x-4




Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
4. Describe the transformations applied to
f%28x%29=x%5E2 to produce the function f%28x%29=2%28x-5%29%5E2%2B10

horizontal shift: right 5 units
vertical shift: up 10 units
reflection about the x-axes: none
reflection about the y-axes: none
vertical stretch or compression: stretched vertically by a factor of 2


5. Convert the following equation into vertex form by completing the square.
f%28x%29+=+2x%5E2%2B12x-4
f%28x%29+=+%282x%5E2%2B12x%29-4
f%28x%29+=+2%28x%5E2%2B6x%29-4
f%28x%29+=+2%28x%5E2%2B6x%2Bb%5E2%29-2b%5E2-4........b=6%2F2=3
f%28x%29+=+2%28x%5E2%2B6x%2B3%5E2%29-2%2A3%5E2-4
f%28x%29+=+2%28x%2B3%29%5E2-18-4
f%28x%29+=+2%28x%2B3%29%5E2-22


Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

To represent an exponent using your keyboard, type the symbol ^

Example:
x^2 means x%5E2


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Problem 4

y = x^2 is the parent quadratic function
y = 2x^2 vertically stretches the curve by a factor of 2
y = 2(x-5)^2 shifts the curve 5 units to the right
y = 2(x-5)^2+10 shifts the curve 10 unit up

Graph:

x^2 in red
2x^2 in green
2(x-5)^2 in blue
2(x-5)^2+10 in purple

Here's a graph of just the parent x^2 and the final result 2(x-5)^2+10
graph%28500%2C500%2C-10%2C10%2C-5%2C15%2Cx%5E2%2C-100%2C-100%2C2%28x-5%29%5E2%2B10%29
I recommend using either Desmos or GeoGebra as a graphing tool.
Both of which are free.

Take notice how the vertex (0,0) in the parent function has been shifted 5 units right and 10 units up to arrive at (5,10) on the final result.

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Problem 5

y = 2x^2+12x-4 is of the form y = ax^2+bx+c
where,
a = 2
b = 12
c = -4

Use the first two values to find the following
h = -b/(2a)
h = -12/(2*2)
h = -3
This is the x coordinate of the vertex (h,k)

Use that to find the y coordinate of the vertex.
y = 2x^2+12x-4
y = 2(-3)^2+12(-3)-4
y = -22
The k value is k = -22

The vertex is located at (h,k) = (-3,-22)

So,
y = a(x-h)^2 + k
y = 2(x-(-3))^2 + (-22)
y = 2(x+3)^2 - 22
represents the vertex form.

Graph:

As mentioned in the previous problem, use graphing software to confirm the answer.