Answer:
Vertex is (3,3)
Axis of symmetry is x=3
Step-by-step explanation:
Given : Function [tex]y = 2x^2 -12x + 21[/tex]
To find : The axis of symmetry and the vertex of the given function.
Solution :
The given function is in the form of quadratic equation [tex]y=ax^2+bx+c[/tex]
Comparing with the given function [tex]y = 2x^2 -12x + 21[/tex]
a=2 , b=-12 and c=21
x-coordinate of axis of symmetry and vertex
Axis of symmetry is given by [tex]x=-\frac{b}{2a}[/tex]
Substitute the value,
[tex]x=-\frac{-12}{2(2)}[/tex]
[tex]x=\frac{12}{4}[/tex]
[tex]x=3[/tex]
For y-coordinate of axis substitute x=3 in y
[tex]y = 2(3)^2 -12(3) + 21[/tex]
[tex]y = 2(9)-36+ 21[/tex]
[tex]y = 18-15[/tex]
[tex]y = 3[/tex]
Therefore, The vertex of function is (3,3).
