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

Equation of the axis of symmetry is:   x = 3

Step-by-step explanation:

The equation

is the equation of a parabola, of the form

   whose vertex is located at the x-coordinate:

Then, for our case the x position of the given parabola, is:

Then the equation of the axis of symmetry, which is a vertical line that goes through the vertex, would be given by:

x = 3

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: