Which equation has an axis of symmetry of 2?(1 point)

Question

Responses

y=−x2+4x+8
y equals negative x squared plus 4 x plus 8

y=−x2+2x+8
y equals negative x squared plus 2 x plus 8

y=x2+4x+8
y equals x squared plus 4 x plus 8

y=x2+2x+8
y equals x squared plus 2 x plus 8
Remaining Attempts : 3

Answer 1

The axis of symmetry for a quadratic equation in the standard form \(y = ax^2 + bx + c\) can be found using the formula:

\[ x = -\frac{b}{2a} \]

Let's analyze each of the given equations to determine which one has an axis of symmetry of \(x = 2\).

1. For the equation \(y = -x^2 + 4x + 8\):

   • Here, \(a = -1\), \(b = 4\).
   • Axis of symmetry: \[ x = -\frac{4}{2(-1)} = -\frac{4}{-2} = 2 \]

2. For the equation \(y = -x^2 + 2x + 8\):

   • Here, \(a = -1\), \(b = 2\).
   • Axis of symmetry: \[ x = -\frac{2}{2(-1)} = -\frac{2}{-2} = 1 \]

3. For the equation \(y = x^2 + 4x + 8\):

   • Here, \(a = 1\), \(b = 4\).
   • Axis of symmetry: \[ x = -\frac{4}{2(1)} = -\frac{4}{2} = -2 \]

4. For the equation \(y = x^2 + 2x + 8\):

   • Here, \(a = 1\), \(b = 2\).
   • Axis of symmetry: \[ x = -\frac{2}{2(1)} = -\frac{2}{2} = -1 \]

From the calculations, the equation that has an axis of symmetry of \(2\) is:

\(y = -x^2 + 4x + 8\).