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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