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

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Determine the axis of symmetry and the vertex of

orlando19882000

11.03.2022

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.

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