A quadratic with a squared expression and a number outside it is in vertex form, which shows shifts from . Find where the square becomes zero for the left-or-right move; the number outside gives the up-or-down move. The inside sign is the trap: it points opposite the horizontal move, while the outside sign follows the vertical move.
Hints
- Hint 1
The vertex is the parabola’s turning point, located at on . The square is zero there. Which new input makes the expression inside the square zero?
- Hint 2
The vertical shift is the up-or-down change to every output. The number outside the square controls it. What happens to a -value when the rule subtracts after squaring?
Step-by-step
Read the shifts from vertex form
Step 1Find the horizontal shift
No Desmos needed. The squared form already shows the shifts. The vertex, or turning point, of is . To find where that point moves horizontally, set the inside of the new square equal to :
Subtract :
So the vertex moves units left, not right. The inside sign points opposite the horizontal move.
- Step 2
Find the vertical shift and answer
The subtraction outside the square lowers every output by ; the parent vertex’s height becomes . So the graph shifts down units. Together, the shifts move the graph units left and units down. Choice B.