A parabola opens upwards if the quadratic coefficient - the number before the "x2" is positive; downward if it is negative. Note that x2 is the same as 1x2.
when you have y=+/-x2 +whatever, the parabola opens up y=-(x2 +whatever), the parabola opens down x=+/-y2 +whatever, the parabola opens right x=-(y2 +whatever), the parabola opens left so, your answer is up
A parabola opening up has a minimum, while a parabola opening down has a maximum.
Upwards.
Finding the vertex of the parabola is important because it tells you where the bottom (or the top, for a parabola that 'opens' downward), and thus where you can begin graphing.
To have a parabola with only one x-intercept, the vertex of the parabola must lie on the x-axis. This means the parabola opens either upwards or downwards, depending on the coefficient of the squared term in the equation. If the coefficient is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards. By adjusting the coefficients in the equation of the parabola, you can position the vertex such that there is only one x-intercept.
when you have y=+/-x2 +whatever, the parabola opens up y=-(x2 +whatever), the parabola opens down x=+/-y2 +whatever, the parabola opens right x=-(y2 +whatever), the parabola opens left so, your answer is up
If the value of the variable is negative then the parabola opens downwards and when the value of variable is positive the parabola opens upward.
if the value is negative, it opens downard
If the equation of the parabola isy = ax^2 + bx + c, then it opens above when a>0 and opens below when a<0. [If a = 0 then the equation describes a straight line, and not a parabola!].
To determine if a parabola opens up or down, look at the coefficient of the quadratic term in its equation, typically in the form (y = ax^2 + bx + c). If the coefficient (a) is positive, the parabola opens upwards; if (a) is negative, it opens downwards. You can also visualize the vertex: if the vertex is the lowest point, it opens up, and if it's the highest point, it opens down.
The given equation of the parabola is in the vertex form (y - 8 = a(x + 5)^2 + 2). Here, (a) is the coefficient of the squared term. Since the coefficient of ((x + 5)^2) is positive (as it's implied to be 1), the parabola opens upwards. Therefore, the parabola opens in the direction of positive y-values.
It is a function because for every point on the horizontal axis, the parabola identified one and only one point in the vertical direction.
The equation that describes a parabola opening left or right with its vertex at the point ((h, k)) is given by ((y - k)^2 = 4p(x - h)), where (p) determines the direction and width of the parabola. If (p > 0), the parabola opens to the right, while if (p < 0), it opens to the left. Here, ((h, k)) represents the vertex coordinates.
To write an equation for a parabola in standard form, use the format ( y = a(x - h)^2 + k ) for a vertical parabola or ( x = a(y - k)^2 + h ) for a horizontal parabola. Here, ((h, k)) represents the vertex of the parabola, and (a) determines the direction and width of the parabola. If (a > 0), the parabola opens upwards (or to the right), while (a < 0) indicates it opens downwards (or to the left). To find the specific values of (h), (k), and (a), you may need to use given points or the vertex of the parabola.
No, a parabola cannot have both a maximum and minimum point. A parabola opens either upwards or downwards; if it opens upwards, it has a minimum point, and if it opens downwards, it has a maximum point. Thus, a parabola can only have one of these extrema, not both.
The given terms can't be an equation without an equality sign but a negative parabola opens down wards whereas a positive parabola opens up wards.
Vertex