Question

Determine the axis of symmetry and the vertex of the given function. y = 2x2 − 12x + 21 Axis of symmetry: x = Vertex: ( , )

Answer 1

The vertex is (3,3) and the axis is 3

Answer 2

Answer:

The vertex of the function is (h,k)=(3,3)

The axis of symmetry is x=3.    

Step-by-step explanation:

Given : Function $y=2x^2-12x+21$

To find : Determine the axis of symmetry and the vertex of the given function.

Solution :  

The quadratic function is in the form, $y=ax^2+bx+c$

On comparing, a=2 , b=-12 and c=21

The vertex of the graph is denote by (h,k) and the formula to find the vertex is

For h, The x-coordinate of the vertex is given by,

$h=-\frac{b}{2a}$

$h=-\frac{-12}{2(2)}$

$h=\frac{12}{4}$

$h=3$

For k, The y-coordinate of the vertex is given by,

$k=f(h)$

$k=2h^2-12h+21$

$k=2(3)^2-12(3)+21$

$k=18-36+21$

$k=3$

The vertex of the function is (h,k)=(3,3)

The x-coordinate of the vertex i.e. $x=-\frac{b}{2a}$ is the axis of symmetry,

So, $x=-\frac{b}{2a}=3$ (solved above)

So, The axis of symmetry is x=3.