What is the equation of the axis of symmetry for the graph of y = (x - 3)^2 + 5?
Check the final answer first, then review the worked steps.
Problem
What is the equation of the axis of symmetry for the graph of y = (x - 3)^2 + 5?
Answer
\(x=3\)
Step-by-step solution
- Identify the form of the equation: The given equation is $y = (x - 3)^2 + 5$. This is the vertex form of a quadratic equation, which is $y = a(x - h)^2 + k$. The vertex form is useful because it directly reveals the vertex of the parabola and its axis of symmetry.
- Determine the vertex: In the vertex form $y = a(x - h)^2 + k$, the vertex of the parabola is located at the point $(h, k)$. Comparing the given equation $y = (x - 3)^2 + 5$ to the general vertex form, we can identify $h = 3$ and $k = 5$. Therefore, the vertex of the parabola is at $(3, 5)$.
- Find the axis of symmetry: For any parabola in the form $y = a(x - h)^2 + k$, the axis of symmetry is a vertical line that passes through the vertex. The equation of this vertical line is always $x = h$. Since we found that $h = 3$, the equation of the axis of symmetry is $x = 3$.