Final answer:
To plot the x-intercepts, y-intercept, vertex, and axis of symmetry for the function g(x) = x^2 + 4x + 3, start by finding the y-intercept, then solve for the x-intercepts using factoring, find the vertex using the formula x = -b/2a, and finally identify the axis of symmetry.
Step-by-step explanation:
To plot the x-intercepts, y-intercept, vertex, and axis of symmetry for the given function g(x) = x^2 + 4x + 3, we can start by finding its y-intercept. The y-intercept is the point where the graph of the function crosses the y-axis and can be found by substituting x = 0 in the function and solving for y. In this case, when x = 0, y = 3, so the y-intercept is (0, 3).
To find the x-intercepts, we can set the function equal to 0 and solve for x. The x-intercepts are the points where the graph crosses the x-axis. In this case, x^2 + 4x + 3 = 0 can be factored as (x + 1)(x + 3) = 0. So, the x-intercepts are -1 and -3.
The vertex of a quadratic function is the highest or lowest point on the graph. It can be found using the formula x = -b/2a, where a and b are the coefficients of the x^2 and x terms, respectively. In this case, a = 1 and b = 4, so x = -4/(2*1) = -2. To find the y-coordinate of the vertex, substitute x = -2 into the function and solve for y. When x = -2, y = 1, so the vertex is (-2, 1).
The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -2.