How do you find the vertex of a parabola #y = x^2 + 3#?

1 Answer
Grégory V.
Jul 10, 2015

the vertex of #f(x)# is #3# when #x=0#

Explanation:

Let #a,b,c#, 3 numbers with #a!=0#

Let #p# a parabolic function such as #p(x) = a*x^2 + b*x + c#

A parabola always admit a minimum or a maximum (= his vertex).

We have a formula to find easily the abscissa of a vertex of a parabola :

Abscissa of vertex of #p(x) = -b/(2a)#
# #
# #
# #
Let #f(x)=x^2+3#
Then, the vertex of #f(x)# is when #0/2=0#
# #
And #f(0) = 3#
# #
# #
Therefore the vertex of #f(x)# is #3# when #x=0#

Because #a>0# here, the vertex is a minimum.

graph{x^2+3 [-5, 5, -0.34, 4.66]}

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