Question

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

Answer 1

f(x)=a(x-h)^2+k. --------->x^3-2hx^2+xh^2+k
f(x)=x^2-8x+20----------->(4,4)

Answer 2

The vertex of the graph f(x)=x^2-8x+20 is (4, 4).

Given, that quadratic function is

$f(x) = x^2 - 8x + 20$ --- (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

$f(x) = x^2 - 8x + 42 - 42 + 20$

Using the algebraic identity

$(a - b)^2 = a^2 + b^2 - 2ab$

We get,

$f(x)= (x - 4)^2 + 4$--- (2)

What is the quadratic function?

$f(x) = a(x - h)^2 + k ,$

where (h, k) is 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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