Question

Which quadratic function has an axis of symmetry of x = 5?y = x^2 + 3x + 5y = -x^2 + 6x + 2y = x^2 + 6x + 3y = x^2 + x + 3

Answer 1

Problem Statement

The question tells us to find the equation of the quadratic function with an axis of symmetry of x = 5.

Method

To solve this question, we need to check each option for which has its vertex at the axis of symmetry.

To find this vertex, we need to follow these steps:

1. Add and subtract half of the square of the coefficient of x.

2. Factorize the result.

3. Find the vertices.

Implementation

Option A:

`\begin{gathered} y=x^2+3x+5 \\ y=x^2+3x+(9)/(4)-(9)/(4)+5 \\ y=(x+(3)/(2))^2+(11)/(4) \\ \\ \text{vertex is:} \\ (-(3)/(2),(11)/(4)) \end{gathered}`

Option B:

`\begin{gathered} y=-x^2+6x+2 \\ y=-x^2+6x+9-9+2 \\ y=-(x-3)^2+9+2 \\ y=-(x-3)^2+11 \\ \\ \text{Vertex:}(3,11) \end{gathered}`

Option C

`\begin{gathered} y=x^2+6x+3 \\ y=x^2+6x+9-9+3 \\ y=(x+3)^2-6 \\ \\ \text{vertex: }(-3,-6) \end{gathered}`

Option D:

`\begin{gathered} y=x^2+x+3 \\ y=x^2+x+(1)/(4)-(1)/(4)+3 \\ y=(x+(1)/(2))^2+(11)/(4) \\ \\ \text{Vertex: }(-(1)/(2),(11)/(4)) \end{gathered}`

Final Answer

THEREFORE, NONE OF THE FUNCTIONS HAVE THEIR AXIS OF SYMMETRY AT X = 5