What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?(,)
(5,-9)
To find the vertex of a quadratic function in the form of f(x) = ax^2 + bx + c, we use the formula:
x = -b / (2a)
y = f(x)
However, in this case, the quadratic function is in factored form, which is f(x) = (x – 8)(x – 2). To find the vertex of this quadratic function, we need to convert it from factored form to standard form by multiplying it out:
f(x) = (x – 8)(x – 2)
f(x) = x^2 – 10x + 16
Now we can see that the quadratic function is in standard form, where a = 1, b = -10 and c = 16. We can substitute these values into the formula to find the vertex.
x = -b / (2a) = -(-10) / (2*1) = 5
y = f(x) = f(5) = 5^2 – 10(5) + 16 = -9
Therefore, the vertex of the quadratic function f(x) = (x – 8)(x – 2) (or f(x) = x^2 – 10x + 16) is (5, -9).
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