What is the vertex of the quadratic function f(x) = 8x – 2?

Finding the Vertex of the Quadratic Function

The vertex of a quadratic function is a crucial point that represents either the maximum or minimum value of the function. In the case of the quadratic function, it can be expressed in the standard form as:

f(x) = ax² + bx + c

In your question, however, it seems there might have been a slight typo, as you mentioned f(x) = 8x – 2, which is technically a linear function instead of a quadratic function. To clarify, let’s assume we want to analyze a standard quadratic function, which might look like this:

f(x) = ax² + bx + c

For the sake of this explanation, let’s use f(x) = 2x² + 8x – 2. Here, we can identify:

• a = 2
• b = 8
• c = -2

Step 1: Calculate the x-coordinate of the Vertex

The formula to find the x-coordinate of the vertex from the coefficients a and b is:

x = -b / (2a)

Plugging in the values we have:

x = -8 / (2 * 2) = -8 / 4 = -2

Step 2: Calculate the y-coordinate of the Vertex

Now, substitute the x-coordinate back into the original function to find the y-coordinate:

f(-2) = 2(-2)² + 8(-2) – 2

f(-2) = 2(4) – 16 – 2 = 8 – 16 – 2 = -10

Step 3: Summarize the Vertex