The vertex form of the equation of a parabola is x=8(y-1)^2-15. What is the standard form of the equation?
huh? multiply
x + 15= 8(y^2 - 2y + 1)
8 y^2 - 16 y + 8 = x +15
x = 8 y^2 - 16 y -7
To find the standard form of the equation of a parabola, we need to expand and simplify the given vertex form equation. In the vertex form, the equation takes the form x = a(y-k)^2 + h, where (h, k) represents the vertex of the parabola.
In the given equation, x = 8(y-1)^2 - 15, we can see that the vertex is at (h, k) = (-15, 1).
To convert it into standard form, we need to expand and simplify the equation.
Start by expanding the squared term:
x = 8(y-1)(y-1) - 15
Simplify the equation:
x = 8(y^2 - 2y + 1) - 15
Distribute the 8:
x = 8y^2 - 16y + 8 - 15
Combine like terms:
x = 8y^2 - 16y - 7
Therefore, the standard form of the equation of the parabola is x = 8y^2 - 16y - 7.