What is the axis of symmetry and vertex given the equation, y=2x^2-12x+21

y = 2x² - 12x + 21 = 2(x² + 6x) + 21.

Using the complet the square method, you get:

2(x² + 6x) + 21 = 2(x² + 6x + 9) - 2*9 + 21 = 2(x + 3)² + 3.

So the axis of symmetry is: x = -3.

The vertex is: (-3, 3)

2(x + 3)² + 3

Explanation: Axis of symmetry: x = -3 Vertex: (-3, 3)

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x