Vertex of upside down parabola |
The vertex of a parabola is the topmost or the bottom-most point of the 'U' curve according to whether the U curve is upside down or upside up. In order to graph a parabola, you need to get the coordinates of the vertex. The coordinates of the vertex of a parabola can be obtained from the quadratic equation/function of that parabola.
Vertex of U shaped parabola |
Let us study the method of calculating the vertex with the help of examples:
A) When the quadratic equation/function is in the general form
When the given quadratic equation/function is in the general form, then you need to get the x and y coordinates of the vertex by the following method:
For any quadratic equation
ax^2 + bx + c = 0,the x coordinate of its vertex is given by:
x = -b/a
For example, in the quadratic function
f(x) = 3x^2 + 4x + 5,the x coordinate of its vertex is
x = -4/3
In order to get the y coordinate of the vertex, we need to substitute the value of the x-coordinate obtained above in place of 'x' in the quadratic. That is, we get
y = 3(-4/3)^2 + 4(-4/3) + 5Therefore the y-coordinate of the vertex is 5.
y = 5
Therefore the coordinates of the vertex are
Vertex = (-4/3, 5).
B) When the quadratic equation/function is given in the vertex form
When the given quadratic is in the vertex form, it is easier to get the coordinates of its vertex directly from the quadratic.
For any quadratic in the vertex form:
f(x) = a(x - h)^2 k,Vertex is given by
Vertex = (h, k)
For example, in the quadratic:
f(x) = 3(x - 4)^2 + 5,the vertex is
vertex = (4, 5)
In a graphical wave form, a parabola which opens up has a lowest point and a parabola which opens down has a highest point and the highest or lowest point on a parabola is called the vertex.
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