Graph transformations take 3 different forms:
- Translations (moving up or down/left or right on a graph)
- Reflections (reflecting the y or x axis)
- Dilations (vertical and horizontal shrinks/stretches)
First, let's discuss translations.
Using the function y=x², you can move a function up/down a graph by adding or subtracting a value.
- To shift an equation up, like the problem asks, rewrite your equation as y=x² + 6
To shift an equation left/right, create parenthesis around the parent equation and either add or subtract a value. Within the parenthesis, the signs act in their opposite fashion. Although an addition sign would usually move a function up or to the right, within the parenthesis, it acts as a subtraction sign, meaning the function would move to the left.
- Using this information, the equation would be rewritten as y=(x²+8) + 6
Now, let's discuss reflections.
Reflections can either be written to flip the function over the y axis (a horizontal flip) or to flip the function over the x axis (a vertical flip).
The question is asking you for a vertical flip over the x-axis, meaning the y values would be negative. To do this, add a negative sign outside the parenthesis of the equation.
Your final answer should be y=-(x²+8) + 6