Identify the vertex for the graph of y = -2x² - 12x + 1.

Solution:

We have to find the vertex of the graph.

For any equation of the type y = ax² + bx + c, the vertex is given by (h, k)

Where, h = -b/2a and k = (4ac - b²)/4a.

Given, the equation is f(x) = -2x² - 12x + 1

Here, a = -2, b = -12 and c = 1

So, h = -(-12)/2(-2)

h = 12/-4

h = -3

4ac = 4(-2)(1)

4ac = -8

So, k = [-8 - (-12)²]/4(-2)

k = (-8 - 144)/-8

k = 152/8

k = 19

Therefore, the vertex is (h, k) = (-3, 19).

Identify the vertex for the graph of y = -2x² - 12x + 1.

Summary:

The vertex of the graph y = -2x² - 12x + 1 is (-3, 19).