Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the following function.

Question

yequalsnegative 3 x squared minus 12 x minus 7
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Part 1
The axis of symmtery is xequals
  
enter your response here. ​(Simplify your​ answer.)

Answer 1

x = -2, the axis of symmetry is x = -2.

To find the axis of symmetry, we use the formula x = -b/(2a) where a = -3 and b = -12.
x = -(-12)/(2*(-3))
x = 12/(-6)
x = -2

Therefore, the axis of symmetry is x = -2.

Answer 2

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the following function.
yequalsnegative 3 x squared minus 12 x minus 7
Question content area bottom
Part 1
The axis of symmtery is xequals
  
negative 2. ​(Simplify your​ answer.)
Part 2
The vertex is
  
enter your response here. ​(Type an ordered pair. Simplify your​ answer.)

Answer 3

For the vertex of a quadratic function in the form y = ax^2 + bx + c, the coordinates of the vertex can be found using the formula (-b/2a, f(-b/2a)), where in this case a = -3 and b = -12.

1. Find the x-coordinate of the vertex:
x = -(-12)/(2*(-3))
x = 12/(-6)
x = -2

2. Plug x = -2 back into the original function to find the y-coordinate of the vertex:
y = -3(-2)^2 - 12(-2) - 7
y = -3(4) + 24 - 7
y = -12 + 24 - 7
y = 5

Therefore, the vertex is at the coordinates (-2, 5).