graph the function. find the vertex line of symmetry, and maximum or minimum value. f(x)=(x+3)^2-4
F(x) = Y = (X + 3)^2 - 4.
Vertex form : Y = a(X - h)^2 + k.
V(h,k) = (-3,-4). a is positive; the
parabola opens upward. Therefore, the
the vertex is at a min. The line of
symmetry = h = -3.
To graph the function f(x) = (x+3)^2 - 4, you can follow these steps:
Step 1: Identify the vertex
The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k, where (h, k) represents the vertex. In our case, the function is already in vertex form, and the vertex is (-3, -4).
Step 2: Determine the line of symmetry
The line of symmetry is vertical and passes through the vertex. In this case, the line of symmetry is x = -3.
Step 3: Find the maximum or minimum value
Since the coefficient of the (x+3)^2 term is positive, the parabola opens upwards, indicating there is a minimum value. The value of the minimum can be read from the k value in the vertex form, which is -4. Therefore, the minimum value is y = -4.
Step 4: Plotting the graph
Now that we have the vertex, line of symmetry, and the maximum or minimum value, we can plot the graph accordingly. Start by plotting the vertex point (-3, -4). Now, choose some x-values on either side of (-3) and substitute them into the equation to find the corresponding y-values. For example, if we choose x = -5, substitute it into the function: f(-5) = (-5+3)^2 - 4 = 4. Hence, we have the point (-5, 4). Similarly, if we choose x = -1, f(-1) = (-1+3)^2 - 4 = 0. So, we have the point (-1, 0). Continue this process and plot more points on both sides of the vertex.
Finally, connect all the points with a smooth curve to obtain the graph of the function f(x) = (x+3)^2 - 4.
Note: The graph should be a U-shaped curve opening upwards. The vertex (-3, -4) will be the low point of the graph. The line x = -3 will be the vertical line of symmetry.