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