y = a(x - h)2 + k is the vertex form of the equation
The vertex is at (h, k)
The axis of symmetry is the vertical line x = h
One of the graphs above has a vertex at (2, - 3)
(h, k)
Use the vertex form to write an equation of the parabola
y =
a(x - h)2 + k use vertex for h and k
y =
a(x - 2)2 + (- 3) Use coordinates of another point
on the parabola for the x and y.
(0, 1)
1=
a(0 - 2)2 + (- 3) Simplify & solve for a
1= a(- 2)2 + (- 3)
+3 + 3
4=
a(- 2)2
4=
4a divide both
sides by 4
1 = a
Write the vertex form again, subbing in a, h, k.
leave xx and yy
y =
a(x - h)2 + k
y =
1 (x - 2)2 - 3
y =
(x - 2)2 - 3
Graphing using the vertex form
y =
- 2(x + 3)2 + 8
Since the number front of the
parenthesis is 2 , you know that the U is turned down and that it is narrow.
The vertex x is OPPOSITE the pos. 3
the vertex y is the same as the constant 8
vertex is ( - 3, 8)
The axis of symmetry is x = - 3
It is always good to know where the graph crosses the axis, so let
x = 0
|
y =
- 2(x + 3)2 + 8
y =
- 2(0 + 3)2 + 8
y =
- 2(3)2 + 8
y =
- 2(9) + 8
y =
- 18 + 8
y =
- 10
Plot (0, - 10) |
That is 3 right of the axis of symmetry, so, you know there is a mirror point 3 left of the axis
-3 + -3 = -6
Plot (- 6, - 10)
|
|
let y = 0, sub in
y = - 2(x + 3)2 + 8
0 = - 2(x + 3)2 + 8
0 = - 2(x2+ 6x + 9) + 8
0 = - 2x2+ -12x + -18 + 8
0 = - 2x2+ -12x + -10
-2 - 2
- 2 - 2
0 =
x2+ 6x + 5
0 = (x +5)(x +1)
x +5= 0
x +1 = 0
- 5 - 5
-1 -1
x
= -5 x
= -1
Plot (-5, 0) and (-1, 0) |
