The vertex form of the parabola y = x² - 2x + 20 is y = ( x - 1 )² + 19 and the vertex is ( 1, 19).
The vertex form of a quadratic function is expressed as:
y = a( x - h )² + k
Where (h, k) is the vertex of the parabola
Given the quadratic equation in the question:
y = x² - 2x + 20
To write the quadratic equation y = x² - 2x + 20 in vertex form, first, we complete the square:
y = x² - 2x + 20
y = ( x² - 2x ) + 20
Add and subtract 1 in the parenthesis:
y = ( x² - 2x + 1 - 1 ) + 20
Factoring, we get:
y = ( x - 1 )² - 1 + 20
y = ( x - 1 )² + 19
Hence, the vertex form of the equation is y = ( x - 1 )² + 19.
Now compare to y = a( x - h )² + k:
Note that; ( h, k ) is the vertex.
y = ( x - 1 )² + 19
Vertex ( h, k ) = ( 1, 19)
Therefore, the vertex of the parabola is ( 1, 19).