What is the vertex of the graph of y = -1(x - 2)² + 3?

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) = -1(x - 2)² + 3

f(x) = -1(x² - 4x + 4) + 3

f(x) = -x² + 4x - 4 + 3

f(x) = -x² + 4x - 1

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

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

h = -4/-2

h = 2

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

4ac = 4

So, k = [4 - (4)²]/4(-1)

k = (4 - 16)/-4

k = -12/-4

k = 3

Therefore, the vertex is (h, k) = (2, 3).

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What is the vertex of the graph of y = -1(x - 2)² + 3?

Summary:

The vertex of the graph f(x) = -1(x - 2)² + 3 is (2, 3).