We have the quadratic equation:
y = -2x² + 8x - 11
We can factorize the first two terms:
y = -2*(x² - 4x) - 11 ...(1)
In the parenthesis term, by completing the square:
x² - 4x = x² - 4x + (4 - 4) = (x - 2)² - 4
Replacing on (1):
y = -2*( (x - 2)² - 4 ) - 11 = -2*(x - 2)² + 8 - 11 = -2*(x - 2)² - 3
y = -2*(x - 2)² - 3 ...(2) => Vertex form
The general vertex form of a quadratic equation is:
y = a*(x - h) + k, where (h, k) is the vertex of the parabola. From our answer above, we identify:
a = -2
h = 2
k = -3
Then, the vertex of the parabola is located at (2, -3). Now, for some x values we have (using equation (2) ):
For x = 0 => y = -11
For x = 1 => y = -5
For x = -1 => y = -21
For x = 2 => y = -3
For x = 3 => y = -5
Then, the table is:
Using this table, we can plot the quadratic function:
