Final answer:
To find the vertex of the quadratic function f(x) = x² - 4x + 3, calculate h = -b/2a, which results in 2. Substituting x = 2 back into the function gives k = -1, making the vertex (2, -1). The line of symmetry is the vertical line x = 2.
Step-by-step explanation:
To find the vertex and the line of symmetry of the quadratic function f(x) = x² - 4x + 3, we need to first put it in vertex form or use the formula for the vertex of a parabola given by a quadratic in standard form ax² + bx + c.
The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) is the vertex of the parabola. The line of symmetry is the vertical line that passes through the vertex, specifically x = h.
For the given function, a = 1, b = -4, and c = 3. The formula for the x-coordinate of the vertex (h) is -b/2a. Substituting the values of a and b, we get h = -(-4)/(2· 1) = 2. Since this is a quadratic with the leading coefficient positive (a = 1), the vertex will be a minimum point. To find the y-coordinate of the vertex (k), we substitute the x-coordinate (h = 2) back into the function: f(2) = (2)² - 4·(2) + 3 = 4 - 8 + 3 = -1. Therefore, the vertex is at (2, -1).
The equation of the line of symmetry is the vertical line x = 2.