Question

Which statement describes the effect on the parabola f(x)=2x•x-5x+3 when changed to f (x)= 2x•2-5x+1

Answer 1

Answer:

The parabola is translated down 2 units.

Step-by-step explanation:

You have the parabola f(x) = 2x² – 5x + 3

To change this parabola to f(x) = 2x² - 5x + 1, you must have performed the following calculation:

f(x) = 2x² – 5x + 3 -2= 2x² - 5x + 1  Expresion A

The algebraic expression of the parabola that results from translating the parabola f (x) = ax² horizontally and vertically is g (x) = a(x - p)² + q, translating in the same way as the function.

• If p> 0 and q> 0, the parabola shifts p units to the right and q units up.
• If p> 0 and q <0, the parabola shifts p units to the right and q units down.
• If p <0 and q> 0, the parabola shifts p units to the left and q units up.
• If p <0 and q <0, the parabola shifts p units to the left and q units down.

In the expression A it can be observed then that q = -2 and is less than 0. So the displacement is down 2 units.

This can also be seen graphically, in the attached image, where the red parabola corresponds to the function f(x) = 2x² – 5x + 3 and the blue one to the parabola f(x) = 2x² – 5x + 1.

In conclusion, the parabola is translated down 2 units.