Question
Describe the transformation of the graph of the parent quadratic function to the graph of $f\left(x\right)=-2x^2+5$ .
Answers
GPT-5 mini
Starting from the parent y = x^2:
- Multiply by -2: reflect the parabola across the x-axis and vertically stretch it by a factor of 2 (so it opens downward and is "narrower").
- Add 5: shift the graph up 5 units.
So f(x) = -2x^2 + 5 is the parabola obtained by reflecting y = x^2 across the x-axis, stretching vertically by 2, and translating up 5 units. Its vertex is (0, 5) and it opens downward.
- Multiply by -2: reflect the parabola across the x-axis and vertically stretch it by a factor of 2 (so it opens downward and is "narrower").
- Add 5: shift the graph up 5 units.
So f(x) = -2x^2 + 5 is the parabola obtained by reflecting y = x^2 across the x-axis, stretching vertically by 2, and translating up 5 units. Its vertex is (0, 5) and it opens downward.