What is the vertex of the graph of y = -4(x + 2)² + 5?

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) = -4(x + 2)² + 5

f(x) = -4(x² + 4x + 4) + 5

f(x) = -4x² - 16x - 16 + 5

f(x) = -4x² - 16x - 11

Here, a = -4, b = -16 and c = -11

So, h = -(-16)/2(-4)

h = 16/-8

h = -2

4ac = 4(-4)(-11)

4ac = 176

So, k = [176 - (16)²]/4(-4)

k = (176 - 256)/-16

k = -80/-16

k = 5

vertex of the graph y = -4(x + 2)^2 + 5

Therefore, the vertex is (h,k) = (2, 5).