How to find the vertex and the intercepts for y = x^2 - 6x + 11?

omreknaqec7

omreknaqec7

Answered question

2023-02-17

How to find the vertex and the intercepts for y = x 2 - 6 x + 11 ?

Answer & Explanation

Jalen Livingston

Jalen Livingston

Beginner2023-02-18Added 7 answers

The constant is 11 so the y intercept is (0,11)
complete the square
let x 2 - 6 x + 11 = 0
( x - 3 ) 2 - 9 + 11 = 0
( x - 3 ) 2 + 2 = 0
hence, the vertex's x coordinate is 3.
Put x=3 into the equation
y = 3 2 - 6 × 3 + 11
y = 9 - 18 + 11
y = 2
So (3,2) is the vertex.
Because it is a positive quadratic, the vertex is a minimum because it is shaped. The minimum does not cross the x axis since it is above the x axis.

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