How to Find the Vertex of a Quadratic Function: Step-by-Step Guide and Example

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

To find the vertex of a quadratic function in the form f(x) = ax^2 + bx + c, we can use the formula x = -b/2a

To find the vertex of a quadratic function in the form f(x) = ax^2 + bx + c, we can use the formula x = -b/2a.

In this case, the quadratic function is f(x) = (x – 8)(x – 2). Let’s first expand and simplify the expression:

f(x) = (x – 8)(x – 2)
f(x) = x^2 – 2x – 8x + 16
f(x) = x^2 – 10x + 16

Comparing this with the general form ax^2 + bx + c, we can see that a = 1, b = -10, and c = 16.

Now, let’s use the formula x = -b/2a to find the x-coordinate of the vertex:

x = -(-10) / (2 * 1)
x = 10 / 2
x = 5

So, the x-coordinate of the vertex is x = 5.

To find the y-coordinate of the vertex, we substitute the x-coordinate we found (x = 5) into the given equation:

f(5) = 5^2 – 10(5) + 16
f(5) = 25 – 50 + 16
f(5) = -9

Therefore, the y-coordinate of the vertex is y = -9.

So, the vertex of the quadratic function f(x) = (x – 8)(x – 2) is V(5, -9).

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