Write an equation of a parabola vertically compressed by a factor of ⅛ and reflected over the x-axis.
Sure, here's an equation for you:
y = -⅛x^2
To find the equation of a parabola that is vertically compressed by a factor of ⅛ and reflected over the x-axis, we can start with the general equation of a parabola:
y = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola.
Since the parabola is vertically compressed by a factor of ⅛, the value of "a" will be ⅛.
Since the parabola is reflected over the x-axis, the value of "a" will be negative.
Let's assume the vertex of the parabola is at (h, k).
Therefore, the equation of the parabola will be:
y = -⅛(x - h)^2 + k
So, the equation of the parabola vertically compressed by a factor of ⅛ and reflected over the x-axis is:
y = -⅛(x - h)^2 + k
To write the equation of a vertically compressed parabola that is reflected over the x-axis, you can start with the general vertex form equation of a parabola:
y = a(x-h)^2 + k
Where (h, k) represents the vertex of the parabola.
Since the parabola is vertically compressed by a factor of ⅛, we need to multiply the coefficient 'a' by ⅛. This will make the parabola narrower and more compressed vertically.
Additionally, since the parabola is reflected over the x-axis, the sign of 'a' will change. If 'a' was positive, it will become negative, and vice versa.
Let's assume the vertex of the parabola is at the coordinates (h, k). Since the parabola is reflected over the x-axis, the sign of 'k' will also change. If 'k' was positive, it will become negative, and vice versa.
Therefore, the equation of the parabola, with a vertical compression and reflection over the x-axis, becomes:
y = -⅛(x-h)^2 - k
So, to find the equation, you just need to substitute the values of h and k with the coordinates of the vertex.
f(x) = x^2
g(x) = -1/8 x^2