Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function.
F(x) = 1/8 (x + 9)² +3
My first math question was written incorrectly.
Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function.
F(x) = 1/5 (x + 9)² +3
3 and x=-2
To find the vertex, line of symmetry, and maximum or minimum value of the function f(x), which is given as f(x) = 1/8(x + 9)² + 3, we can follow these steps:
Step 1: Identify the vertex form of the function.
The vertex form of a quadratic function is given as f(x) = a(x - h)² + k, where (h, k) represents the coordinates of the vertex.
By comparing f(x) with the vertex form, we can identify that a = 1/8, h = -9, and k = 3.
Step 2: Find the vertex.
The x-coordinate of the vertex can be found by setting x - h = 0, so x = -(-9) = 9. The y-coordinate of the vertex is simply k, which is 3.
Therefore, the vertex of the function is (9, 3).
Step 3: Determine the line of symmetry.
The line of symmetry is a vertical line that passes through the vertex, and it is always in the form x = h when the vertex is (h, k).
Hence, the line of symmetry for this function is x = 9.
Step 4: Identify the maximum or minimum value.
Since the coefficient of the squared term (x + 9)² is positive (1/8 > 0), the function opens upwards, which means it has a minimum value.
The y-coordinate of the vertex represents the minimum value of the function. In this case, the minimum value is 3.
Step 5: Graph the function.
To graph the function, plot the vertex (9, 3), and then choose a few more x-values on either side of the vertex. Calculate the corresponding y-values for each x-value using the function.
For example:
When x = -6:
f(x) = 1/8((-6) + 9)² + 3 = 1/8(3)² + 3 = 1/8(9) + 3 = 1 + 3 = 4
So, when x = -6, f(x) = 4.
You can repeat this step for a few more x-values to get additional points.
Finally, plot these points on a graph and connect them smoothly. The resulting graph will be a U-shaped curve with the vertex at (9, 3) and the line of symmetry at x = 9.