The vertex of the graph of the function [tex]f(x)=2(x-2)^2+3[/tex] is at (2, 3). This is obtained by comparing the given function of the graph with the vertex form function of a parabola.
What is the vertex of a parabola?
- The vertex of a parabola is the point of intersection of the parabola and its line of symmetry.
- For a parabola whose equation is given in the standard form [tex]y=ax^2+bx+c[/tex], then the vertex will be the minimum of the graph if a>o and the maximum of the graph if a<0.
- The vertex form of a parabola is [tex]y=a(x-h)^2+k[/tex]. Where (h, k) is said to be the vertex of the graph.
Finding the vertex:
Given that the function of the graph is [tex]f(x)=2(x-2)^2+3[/tex].
We have the vertex form as [tex]y=a(x-h)^2+k[/tex]
So, the graph shows a parabola for the given equation.
On comparing the given equation with the vertex form,
f(x)=y, a=2, h=2, and k=3.
Then, (h, k)=(2, 3)
It is shown in the graph below.
Therefore, the vertex of the graph is at the point (2, 3).
Learn more about the vertex of a graph here:
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