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

Question

Ethan Adkins · Accepted Answer

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

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 can never have a maximum or a minimum (i.e., its vertex).

We possess a formula that makes determining the abscissa of a parabola's vertex effortless:

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.

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

Jameson Allen · Answer

undefined To find the vertex of the parabola y = x^2 + 3, you use the formula for the x-coordinate of the vertex, which is given by x = -b/(2a), where a is the coefficient of the x^2 term and b is the coefficient of the x term. In this equation, a = 1 and b = 0. Then, substitute these values into the formula to find the x-coordinate of the vertex. After finding the x-coordinate, substitute it back into the equation of the parabola to find the y-coordinate. Therefore, the vertex of the parabola y = x^2 + 3 is (0, 3).