Finding the Vertex of a Quadratic Function: Step-by-Step Guide with Examples

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 f(x) = a(x – h)^2 + k, we can use the formula: (h, k). In this case, the given quadratic function is f(x) = (x – 8)(x – 2).

To determine the vertex, we need to rewrite the equation in the standard vertex form f(x) = a(x – h)^2 + k. Expanding the given equation, we get:

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

Now we can see that the coefficient of x^2 is 1, which is equal to “a” in the vertex form equation. The coefficient of x, “b,” is -10, and the constant term is 16.

To find the x-coordinate of the vertex, we use the formula:
h = -b / (2a)

In this case:
h = -(-10) / (2 * 1)
= 10 / 2
= 5

Now to find the y-coordinate of the vertex, we substitute the x-coordinate (h) back into the original equation:
f(x) = x^2 – 10x + 16

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

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

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