Finding the Vertex of a Quadratic Function | Step-by-Step Guide with 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 of f(x) = (x – a)(x – b), we need to first rewrite the function in standard form, which is f(x) = ax^2 + bx + c

To find the vertex of a quadratic function in the form of f(x) = (x – a)(x – b), we need to first rewrite the function in standard form, which is f(x) = ax^2 + bx + c.

Given that f(x) = (x – 8)(x – 2), we can expand this expression using the distributive property:

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

Now, we can identify the values of a, b, and c for this quadratic function. In this case, a = 1, b = -10, and c = 16.

The x-coordinate of the vertex can be found using the formula x = -b / (2a). Plugging in the values, we have:

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

To find the y-coordinate of the vertex, we substitute this value of x back into the original function:

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

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

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