Question

Determine the vertex of the quadratic relation y=2(x+2)(x-6).

Answer 1

V = (2,-32)

Explanation:

Hello!

The vertex of a quadratic lies on the Axis of Symmetry (AOS). The axis of symmetry is exactly in the middle of the roots of the Quadratic. We can solve for the AOS by finding the average of the two roots.

Roots

• y = 2(x + 2)(x - 6)
• 0 = 2(x + 2)(x - 6)
• 0 = (x + 2)(x - 6)
• 0 = x + 2: x = -2
• 0 = x - 6: x = 6

The two roots of the quadratic are 6 and -2.

Solve for the AOS

• 
  `AOS = (r_1 + r_2)/(2)`
• 
  `AOS = (6-2)/(2)`
• 
  `AOS = \frac42`
• 
  `AOS = 2`

The Axis of symmetry of the quadratic is 2.

Vertex

Since the vertex lies on the AOS, we know the x-value of the vertex. We can solve for the y-value by plugging in the value of the AOS in the equation.

Find the Vertex

• y = 2(x + 2)(x - 6)
• y = 2(2 + 2)(2 - 6)
• y = 2(4)(-4)
• y = 2(-16)
• y = -32

The Vertex of the quadratic is at (2,-32).