Draw the graph of the polynomial f(x) = -4x²+4x-1. Also find the vertex of this parabola

x -2 -3/2 -1 -1/2 0 1/2 1 3/2 2 5/2

y -25 -16 9 -4 -1 0 -1 -4 -9 -16

srisaji@yahoo.com

Answer :

We have polynomial y  = -4x² + 4x - 1 
For vertex we use formula As :
h = $-\frac{b}{2a}$ , here a  = -4  And b = 4 
So ,
h = $\frac{1}{2}$ 
SO, the axis of symmetry is x  = ​$\frac{1}{2}$   = 0.5
Put that value in our given polynomial and get
y  = -4 ( ​$\frac{1}{2}$  )² + 4 ( ​$\frac{1}{2}$  ) - 1
y  = -1 + 2 -1 
y  = 0
So,
The vertex is ( 0.5 , 0 )                                  ( Ans )

Step 1 - Now form a table , with different values of x and y As :

y  = -4x2 + 4x - 1
x	y
-2	-25
-1.5	-16
-1	-9
-0.5	-4
0	-1
0.5	0
1	-1
1.5	-4
2	-9

Step - 2 plot these poit on x -y plane and get