For each parabola, tell in which direction the graph opens.
x= 1/2y^2
y= -1/24x^2
a. as y increaese, x increases, so opens up.
b. as x increases, y goes more negative...opens down.
(a) as y increases, x increases, so it opens to the right
To determine the direction in which a parabola opens, you can look at the coefficient of the squared variable.
1. For the equation x = 1/2y^2:
- The coefficient of the squared variable (y^2) is positive (1/2).
- When the coefficient is positive, the parabola opens upwards, resembling a "U" shape.
2. For the equation y = -1/24x^2:
- The coefficient of the squared variable (x^2) is negative (-1/24).
- When the coefficient is negative, the parabola opens downwards, resembling an upside-down "U" shape.
Remember, the coefficient of the squared variable determines the direction in which the parabola opens. If the coefficient is positive, the parabola opens upwards, and if the coefficient is negative, the parabola opens downwards.