Question

y = 2(x + 4)^2 - 3

1. describe in words the transformation of the following quadratic. you must use terminology learned in class: vertical/horizontal translation; units up/down and right/left; vertical stretch by factor; vertical reflection or reflection over x - axis.

y = -x^2 - 5

y = 3x^2 + 1

y = \frac{1}{2}(x + 5)^2 - 2

y = -2(x - 3)^2 + 4

Explanation:

For each quadratic, compare to parent function $y=x^2$:

1. $y=-x^2-5$: Negative sign reflects over x-axis; -5 shifts down 5 units.
2. $y=3x^2+1$: 3 is a vertical stretch factor; +1 shifts up 1 unit.
3. $y=\frac{1}{2}(x+5)^2-2$: $\frac{1}{2}$ is vertical shrink; +5 shifts left 5; -2 shifts down 2.
4. $y=-2(x-3)^2+4$: -2 reflects over x-axis and stretches by 2; -3 shifts right 3; +4 shifts up 4.

Answer:

1. Reflection over the x-axis, vertical translation 5 units down
2. Vertical stretch by a factor of 3, vertical translation 1 unit up
3. Vertical shrink by a factor of $\frac{1}{2}$, horizontal translation 5 units left, vertical translation 2 units down
4. Reflection over the x-axis, vertical stretch by a factor of 2, horizontal translation 3 units right, vertical translation 4 units up