Using the specific transformation from y=x^2 Write this in vertex form:Vertical stretch of 2, reflect across the x axis and 3 units up

Answer 1

The "generic" vertex form is y = a(x - h)² + k where the vertex is the point (h, k) and the vertical stretch is the "a" value. Additionally, a negative in front of the a will reflect the graph across the x-axis. Since the vertex is the point (h, k), the "h" is the horizontal shift and "k" is the vertical shift. The reason for that is that the vertex of y = x² is at the origin (0, 0) and since the vertex essentially becomes the "new origin", the shift is "h" in the x-direction and "k" in the y-direction.

At any rate, this makes the vertex form:

y = -2(x - 0)² + 3 or I suppose you could write it like this:

y = -2x² + 3 but this isn't as obviously in vertex form as the other

Answer 2

y=x²

Vertical stretch by 2

y=2x²

Refection on the x axis

y=-2x²

3 units up

y=-2x²+3