What are the coordinates of the vertex of the graph of the function y = -3x² - 12x + 3?

Solution:

We have to find the coordinates of the vertex.

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 y = -3x² - 12x + 3

Here, a = -3, b = -12 and c = 3

So, h = -(-12)/2(-3)

h = 12/(-6)

h = -2

4ac = 4(-3)(3)

4ac = -36

So, k = [-36 - (-12)²]/4(-3)

k = (-36 - 144)/(-12)

k = -180/-12

k = 15

Therefore, the coordinates of the vertex is (h, k) = (-2, 15).

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What are the coordinates of the vertex of the graph of the function y = -3x² - 12x + 3?

Summary:

The coordinates of the vertex of the graph of the function y = -3x² - 12x + 3 are (-2, 15).