How do you find the vertex of the following:?

Question

y=x^2-9x

y=3x-8x+1

please give details :)

Answer 1

there is a simple method in which you can use to find the vertexof a parabola.

For any parabola, the general equation is ax^2 + bx + c = 0

Firstly, find the axis of symmetry by using the formula:

x= -b

     ---

     2a

then substitute the value of x (i.e the axis of symmetry) into the equation of the parabola to obtain the y value

E.G.

y=3x^2-8x+1

General formula: ax^2 + bx + c = 0

hence, y=3x^2-8x+1 and ax^2 + bx + c = 0 are equivalent,

a= 3, b=-8, c= 1

Axis of symmetry: x = -b

                                ------

                                 2a

                           x = - (-8)

                                 -------

                                   2(3)

                              =   1 1/3

Substitue x= 1 1/3 into the equation y=3x^2-8x+1

y=3x^2-8x+1

y= 3 (1 1/3 )^2 -8(1 1/3) +1

  = -4 1/3

Thus the vertex for this equation is (1 1/3, -4 1/3)

i hope this method of finding the vertex will help you with all the other parabolas

All the best :)