Multiplying a function value by a constant effectively applies a vertical scale factor to that function. The scale factor is the constant. Here, the parent function x² is multiplied by 1/2 (to give 1/2x²). The vertical scale factor is 1/2.
Adding a constant to a function value causes a vertical translation of that function. Every output value is moved upward (translated) by the amount that is added. Here, that added amount is -5, so the vertical movement is downward 5 units.
For f(x) = x², vertical scaling by a factor of 1/2 makes it 1/2x². Translating that downward 5 units makes it ...
... y = 1/2x² - 5 . . . . . . . . . x² scaled and translated
