Write the quadratic function in the form f(x) = a(x - h)² + k. Then give the vertex of its graph f(x)  =x² - 8x + 20

Solution:

Given, quadratic function is

f(x) = x² - 8x + 20 --- (1)

We know that the vertex form is

f(x) = a(x - h)² + k

The vertex of the graph is given by (h, k)

The equation (1) can also be written by completing the square as

f(x) = x² - 8x + 4² - 4² + 20

Using the algebraic identity

(a - b)² = a² + b² - 2ab

We get

f(x)= (x - 4)² + 4 --- (2)

We know f(x) = a(x - h)² + k ,

where (h, k) are the vertex.

Comparing both the equations we get, the vertex as

(h, k) = (4, 4)

Therefore, the vertex of the graph is (4, 4).

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Write the quadratic function in the form f(x) = a(x - h)² + k. Then give the vertex of its graph f(x) = x² - 8x + 20

Summary:

The quadratic function in the form f(x) = a(x - h)² + k is f(x) = (x - 4)² + 4. Then the vertex of its graph f(x) = x² - 8x + 20 is (4, 4).