Now we can simplify the right-hand side by completing the square. We have to add and subtract ( b2)^2. In this case, we have that the linear coefficient b is 4.
b=4 ⇒ (b/2)^2=(4/2)^2=2^2
We can see that the y-variable is raised to the power of 1 and the x-variable is raised to the power of 2. Therefore, the equation matches the format of a verticalparabola.
Standard Form:& y= a(x- h)^2+ k [0.8em]
Equation:& y= 3(x-( - 2))^2+( - 4)
The vertex of this type of parabola is the ordered pair ( h, k). Therefore, the vertex of the given parabola is ( - 2, - 4).
To draw its graph, we need to calculate the focus and the directrix.
Focus
Directrix
( h, k+1/4 a )
y= k-1/4 a
( - 2, - 4+1/4( 3)) ⇕ (- 2,- 3 1112)
y= - 4-1/4( 3) ⇕ y=- 4 112
Finally, to obtain an accurate graph, we will find two more points on the parabola. We will arbitrarily choose two values for x and calculate their corresponding y-value.
x
3(x-(- 2))^2+(- 4)
y=3(x-(- 2))^2+(- 4)
- 4
3( - 4-(- 2))^2+(- 4)
8
0
3( 0-(- 2))^2+(- 4)
8
Let's use the obtained information to draw a graph!
