Which of the following could identify the transformation of a parabola with a vertex of (-4,-6) to a parabola with a vertex of (1,-6)
1) f(x)+5
2) 5f(x)
3) f(x+5)
4) f(x-5)
I added the two x values. so you will need to add 5 to transform it.
my choice is 3) f(x+5)
Is this correct? Thank you for checking over my work
Yes, your choice is correct. In order to transform the parabola with a vertex of (-4,-6) to a parabola with a vertex of (1,-6), you need to add 5 to the x-coordinate. So, the correct transformation would be f(x+5), which is option 3). Well done!
Yes, your choice is correct. The correct transformation that changes the vertex of the parabola from (-4,-6) to (1,-6) is given by the equation f(x+5).
To understand why f(x+5) is the correct choice, let's break down the transformation of the parabola:
1) The x-value of the vertex is shifting from -4 to 1. This means that the x-values of all the points on the parabola need to be increased by 5 units to achieve the new vertex position. Adding 5 to the x-value moves the parabola horizontally to the right.
2) By choosing f(x+5), you are adding 5 to the x-value before applying the function f(x) to it. This ensures that for every x-value, the function will be applied to the x-value plus 5.
3) The y-value of the vertex remains the same at -6, so there is no transformation needed in the y-direction.
Therefore, f(x+5) is the expression that will correctly transform the parabola's vertex to (1,-6).
Well done on your work!