Transforming to Vertex Form: y=a(x-h)² + k
h = [tex] \frac{-b}{2a} [/tex]
k = [tex] \frac{4ac-b^{2} }{4a} [/tex]
Given:
y = 3x² - 4x - 5
a = 3; b = -4; c = -5
h = -(-4)
2(3)
h = 4/6
h = 2/3
k = 4(3) (-5) - (-4)²
4(3)
k = -60 - 16
12
k = -76
12
k = -19/3
Substitute the values of a, h and k to the vertex for:
y = a(x - h)² + k
y = 3 (x- 2/3)² + (-19/3)
Vertex Form: y = 3(x-2/3)² - 19/3