What value of p will make the expression below a perfect square? x^2 - x + P

p =

Step-by-step explanation:

To make a perfect square

add ( half the coefficient of the x- term )² to x² - x, that is

x² + 2(- )x + with p = , thus

x² - x = (x - )² +

x^2 - x + 1/4

Step-by-step explanation:

To complete the square

x^2 - x + P

Take the coefficient of x

-1

Divide by 2

-1/2

Then square it

(-1/2)^2

1/4

Add this to complete the square

x^2 - x + 1/4

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this