What is the vertex of the parabola given by y = -(x - 2)² - 1?

Solution:

We have to find the vertex of the parabola.

For any parabola 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 = -(x - 2)² - 1

y = -(x² - 4x + 4) - 1

y = -x² + 4x - 4 - 1

Y = -x² + 4x - 5

Here, a = -1, b = 4 and c = -5

So, h = -4/2(-1)

h = -4/-2

h = 2

4ac = 4(-1)(-5)

4ac = 20

So, k = [20 - (4)²]/4(-1)

k = (20 - 16)/-4

k = 4/-4

k = -1

Therefore, the vertex is (2, -1).

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What is the vertex of the parabola given by y = -(x - 2)² - 1?

Summary:

The vertex of the parabola given by y = -(x - 2)² - 1 is (2, -1).