Answer:
Step-by-step explanation:
Given equation
To find
The constants p, q, r when
- 3x² - 4x + 6 = p(x - q)² + r
Solution
The least value is at vertex of the parabola ax² + bx + c, with positive a
x and y -coordinates of the vertex is:
- x = -b/2a = - (-4)/(2*3) = 2/3
- y = 3(2/3)² - 4(2/3) + 6 = 3(4/9) - 8/3 + 6 = 4/3 - 8/3 + 6 = 14/3
The vertex form is:
- y = a(x-h)² + k, where (h, k) is the vertex
Applying the same formula to our equation:
- 3x² - 4x + 6 = 3(x - 2/3) + 14/3
The constants p, q and r are:
