Table to Equation – Method Two (use the coordinates of the vertex and any other point)
Using the roots, write an equation in vertex form where h = 1 and k = -8.
The vertex is (h, k).
y = a(x - h)2 + k
y = a(x - 1)2 - 8
x |
y |
Critical attribute |
-2 |
10 |
|
-1 |
0 |
x-intercept |
0 |
-6 |
y-intercept |
1 |
-8 |
Vertex (minimum) |
2 |
-6 |
Symmetric point |
3 |
0 |
x-intercept |
4 |
10 |
To find the value of 'a,' use coordinates of any other point on the graph:
Note: x-values are in red and y-values are in green and a-values are in blue
y-intercept is (0, -6)
-6 = a(0 - 1)2 - 8
-6 = a(- 1)2 - 8
-6 = a(1)- 8
-6 + 8= a - 8 +8
2 = a
Therefore, the particular equation for this table is:
y = 2(x - 1)2 - 8
y = 2(x2 - 2x + 1) - 8
y = 2x2 - 4x + 2 - 8
y = 2x2 - 4x - 6
Both methods yield the same equation.