Question

Express f(x) = -x-4x+ 12 in the vertex form, fix) = ax + h)²+ k, and in the intercept form, flx)= a(x + p)(x +q). where a, h, k, p and q are constants. Hence, sketch the graph..

Answer 1

You really should proofread what you post. I'll go with
-x^2 - 4x + 12
-(x^2 + 4x) + 12
-(x^2 + 4x + 4) + 12 + 4
-(x+2)^2 + 16

-x^2 - 4x + 12
-(x^2 + 4x - 12)
-(x+6)(x-2)

There are lots of handy online graphing sites if you need help with that.

Answer 2

If your question means:

Express f(x) = - x² - 4 x + 12

then

add and subtract 4 to left side

f(x) = - x² - 4 x + 12 + 4 - 4

f(x) = - x² - 4 x - 4 + 12 + 4

f(x) = - ( x² + 4 x + 4 ) + 16

f(x) = - ( x² + 2 ∙ x ∙ 2 + 2² ) + 16

Since:

( a + b )² = a² + 2 ∙ a ∙ b + b²

( x + 2 )² = x² + 2 ∙ x ∙ 2 + 2²

f(x) = - ( x + 2 )² + 16


f(x) = a ( x - p ) ( x - q )

where p and q are the roots:

In this case:

a = - 1

- ( x + 2 )² + 16 = 0

Subtract 16 to both sides

- ( x + 2 )² = - 16

Multiply both sides by - 1

( x + 2 )² = 16

x + 2 = ± √16

x + 2 = ± 4

Subtract 2 to both sides

x = ± 4 - 2

The solutions are:

p = 4 - 2 = 2

q = - 4 - 2 = - 6

f(x) = ( - 1 ) ( x - p ) ( x - q )

f(x) = - ( x - 2 ) [ ( x - ( - 6 ) ]

f(x) = - ( x - 2 ) ( x + 6 )