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1 year ago

Describe the transformations from the parent function f(x)=x2 to the function g(x)=(x-2)^2+5

Mathematics

1 answer:

Pani-rosa [81]1 year ago

8 0

Answer:

C.) 2 units to the right, 5 units up

Step-by-step explanation:

The graph shifts left or right when a number modifies the "x" value before it is affected by any other number/function in the equation. This number is within parentheses with the "x". Subtracting a value moves the function to the right, whereas adding a value moves the function to the left. Therefore, since 2 is being subtracted from "x", the function has been shifted 2 units to the right.

The graph shifts up or down when the y-intercept changes. The y-intercept is the "b" value in a standard function. You can identify this value by plugging in zero to "x". If this number is positive, the function is shifted upwards, and if this number is negative, the function is shifted downwards. Therefore, since there is a 5 added to the equation, the function is shifted 5 units up.

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Complete the square:

$x^2-8x+a^2\implies a=\dfrac{8x}{2x}=4\implies x^2-8x+4^2\\\\\\y^2-6y+b^2\implies b=\dfrac{6y}{2y}=3\implies y^2-6y+3^2$

And we have:

$(x^2-8x)+(y^2-6y)=-24\\\\(x^2-8x+4^2)-4^2+(y^2-6y+3^2)-3^2=-24\\\\
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3 years ago

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2 years ago