SOLUTION: If the parabola has equation y = 2(x - 4)? - 1 as a base function, write an equation for the parabola if there is a reflection in the x-axis followed by a translation of 3 units u

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Question 1202232: If the parabola has equation y = 2(x - 4)? - 1 as a base function, write an equation for the
parabola if there is a reflection in the x-axis followed by a translation of 3 units upwards.
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
If the parabola has equation y = 2(x-4)^2 - 1 as a base function, write an equation for the
parabola if there is a reflection in the x-axis followed by a translation of 3 units upwards.
~~~~~~~~~~~~~~~~~~~~~~ 

First, reflection in the x-axis turns the function into

    y = -2(x-4)^2 + 1.


    +---------------------------------------------------------------+
    |   It simply changes the sign of all terms in the right side.  |
    +---------------------------------------------------------------+


So, after this transformation our function is

    y = -2(x-4)^2 + 1.    (1)


The translation of 3 units upwards adds 3 to the function (1),
so after this translation your function is

    y = -2(x-4)^2 + 4.    ANSWER

The problem is SOLVED.

Please write me if you get all my explanations in full.