Above
right
The vertex of a parabola that opens down is called the maximum point. This point represents the highest value of the function described by the parabola, as the graph decreases on either side of the vertex. In a quadratic equation of the form (y = ax^2 + bx + c) where (a < 0), the vertex can be found using the formula (x = -\frac{b}{2a}). The corresponding (y)-value can then be calculated to determine the vertex's coordinates.
5
3
To find the value of a in a parabola opening up or down subtract the y-value of the parabola at the vertex from the y-value of the point on the parabola that is one unit to the right of the vertex.
right
Above
When you look at the parabola if it opens downwards then the parabola has a maximum value (because it is the highest point on the graph) if it opens upward then the parabola has a minimum value (because it's the lowest possible point on the graph)
The vertex of a parabola that opens down is called the maximum point. This point represents the highest value of the function described by the parabola, as the graph decreases on either side of the vertex. In a quadratic equation of the form (y = ax^2 + bx + c) where (a < 0), the vertex can be found using the formula (x = -\frac{b}{2a}). The corresponding (y)-value can then be calculated to determine the vertex's coordinates.
The vertex of this parabola is at -2 -3 When the y-value is -2 the x-value is -5. The coefficient of the squared term in the parabola's equation is -3.
The vertex of this parabola is at 5 5 When the x-value is 6 the y-value is -1. The coefficient of the squared expression in the parabola's equation is -6.
3
5
Yes if it is positive
A quadratic equation in vertex form is expressed as ( y = a(x - h)^2 + k ), where ((h, k)) is the vertex of the parabola. For a parabola with vertex at ((11, -6)), the equation becomes ( y = a(x - 11)^2 - 6 ). The value of (a) determines the direction and width of the parabola. Without additional information about the parabola's shape, (a) can be any non-zero constant.
-5