Question

drag the point to show how much you agree/disagree with this statement:
y = -(x - 3)^2 + 1
opens down
shifts down 3
shifts right 1
if you disagree, write what is correct and what is incorrect.

Explanation:

Step1: Recall vertex form rules

The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \( a \) determines direction, \( h \) horizontal shift, \( k \) vertical shift.

Step2: Analyze \( a \) for direction

For \( y = -(x - 3)^2 + 1 \), \( a=-1<0 \), so opens down (correct).

Step3: Analyze horizontal shift (\( h \))

Here \( h = 3 \), so shift right 3 (incorrect, stated right 1).

Step4: Analyze vertical shift (\( k \))

Here \( k = 1 \), so shift up 1 (incorrect, stated down 3).

Answer:

Disagree. Correct: Opens down, shifts right 3, shifts up 1. Incorrect: Shifts down 3, shifts right 1.