Question
ERROR ANALYSIS Describe and correct the error in analyzing the graph of $f\left(x\right)=-6x^2+4$ .
X The graph is a reflection in the y-axis and a vertical stretch by a factor of 6, followed by a translation 4 units up of the graph of the parent quadratic function.
X The graph is a reflection in the y-axis and a vertical stretch by a factor of 6, followed by a translation 4 units up of the graph of the parent quadratic function.
Answers
GPT-5 mini
Error: the negative sign reflects across the x-axis, not the y-axis. A reflection in the y-axis would come from replacing x by −x (e.g. x^2 → (−x)^2), which does not occur here.
Correct description: start with y = x^2. Multiply by 6 (vertical stretch by a factor of 6), then multiply by −1 (reflection across the x-axis) to get y = −6x^2, and finally translate up 4 units to get y = −6x^2 + 4. (Reflection across the x-axis and the vertical stretch can be viewed together as a single multiplication by −6.) The graph is a downward-opening parabola, narrower than y = x^2, with vertex at (0, 4).
Correct description: start with y = x^2. Multiply by 6 (vertical stretch by a factor of 6), then multiply by −1 (reflection across the x-axis) to get y = −6x^2, and finally translate up 4 units to get y = −6x^2 + 4. (Reflection across the x-axis and the vertical stretch can be viewed together as a single multiplication by −6.) The graph is a downward-opening parabola, narrower than y = x^2, with vertex at (0, 4).