Final answer:
The vertex of the quadratic function is (-2, 1). The x-intercepts are -1 and -3. The y-intercept is 3.
Step-by-step explanation:
To find the vertex of the quadratic function f(x) = x² + 4x + 3, we can use the formula x = -b/2a. In this case, a = 1, b = 4, and c = 3. Thus, the x-coordinate of the vertex is x = -4/(2*1) = -2. To find the y-coordinate, we substitute the x-coordinate back into the equation: f(-2) = (-2)² + 4(-2) + 3 = 1. Therefore, the vertex is (-2, 1).
To find the x-intercepts, we set f(x) = 0 and solve for x. In this case, x² + 4x + 3 = 0. Using the quadratic formula, x = (-b ± √(b² - 4ac))/(2a). Substituting the values of a = 1, b = 4, and c = 3 into the formula, we get x = (-4 ± √(4² - 4*1*3))/(2*1). Simplifying the expression inside the square root, we have x = (-4 ± √(16 - 12))/2. This becomes x = (-4 ± √4)/2. Taking the square root, we get x = (-4 ± 2)/2. So, x = (-4 + 2)/2 = -1 and x = (-4 - 2)/2 = -3. Therefore, the x-intercepts are -1 and -3.
To find the y-intercept, we substitute x = 0 into the equation: f(0) = (0)² + 4(0) + 3 = 3. Therefore, the y-intercept is 3.