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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) = -4×2 – 16x – 16 + 5

f(x) = -4×2 – 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

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

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

Summary:

The vertex of the graph y = -4(x + 2)2 + 5 is (2, 5).

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