Y = (x – 4)2 + 5
D:
R:

= ( − 4 ) 2 + 5

Step-by-step explanation:

Direction: Opens Up

Vertex:  

( 4 , 5 )

Focus:  ( 4, 21 4)

Axis of Symmetry:  x =4

Directrix:  y = 19 4

Select a few

x

values, and plug them into the equation to find the corresponding

y

values. The  

x

values should be selected around the vertex.

Tap for more steps... x y 2 9 6 4 5 5 6 9

Graph the parabola using its properties and the selected points.

Direction: Opens Up

Vertex:  ( 4 , 5 )

Focus:  ( 4 , 21 4 )

Axis of Symmetry:  x = 4

Directrix:  y = 19 4 xy 2 9 3 64 5 5 6 6 9

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