Question

Can someone help me with both these qeustions?

Answer 1

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