Question

What is the vertex form of `y=x^2-5x+4`?

Answer 1

`y = (x - 5/2 )^2 - 9/4`

Explanation:

the standard form of a quadratic function is `ax^2 + bx + c`

the function `y = x^2 -5x + 4 " is in this form "`

by comparison: a = 1 , b = - 5 and c = 4

the vertex form of the function is `y = (x-h)^2 + k`

where (h,k) are the coords of the vertex.

x-coord (h) = `(-b)/(2a) = -(-5)/2 = 5/2`

and y-coord ( k ) = `(5/2)^2 - 5(5/2) + 4 = -9/4`

here ( h, k) = (`5/2 , -9/4 ") and " a = 1`

`rArr y = (x - 5/2 )^2 - 9/4 " is the equation "`