Answer:
a) (2, -8)
Explanation:
The parabolas are given in standard form:
y = ax² + bx + c
We need to convert them to vertex form:
y = a (x − h)² + k
One option is to complete the square.
Another option is to find the x-coordinate of the vertex using h = -b/2a, then plug in to find the y-coordinate of the vertex (k).
Using the second method:
a) a = 3, b = -12
h = -(-12) / (2×3)
h = 2
k = 3(2)² − 12(2) + 4
k = -8
So the vertex is at (2, -8), and the vertex form is:
y = 3 (x − 2)² − 8
We can check our answer by distributing:
y = 3 (x² − 4x + 4) − 8
y = 3x² − 12x + 12 − 8
y = 3x² − 12x + 4