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 x-coordinate of the vertex
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 x-coordinate of the vertex.
In the given quadratic function f(x) = (x – 8)(x – 2), we can rewrite it in the form 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 find the x-coordinate of the vertex using the formula x = -b / (2a):
x = -(-10) / (2 * 1)
x = 10 / 2
x = 5
So, the x-coordinate of the vertex is 5.
To find the y-coordinate of the vertex, we substitute the x-coordinate into the equation f(x):
f(5) = (5)^2 – 10(5) + 16
f(5) = 25 – 50 + 16
f(5) = -9
Therefore, the y-coordinate of the vertex is -9.
The vertex of the quadratic function f(x) = (x – 8)(x – 2) is (5, -9).
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