The vertex of the graph is (h, k) = (- 2, 36).
<h3>How to find analytically the vertex of a quadratic equation</h3>
In this question we have a quadratic equation of the form f(x) = a · (x - r₁) · (x - r₂) and we need to transform the expression into its vertex form of determine the coordinates of the vertex. First, we need to exprand the expression:
f(x) = - 4 · (x - 1) · (x + 5)
f(x) = - 4 · (x² + 4 · x - 5)
f(x) = - 4 · x² - 16 · x + 20
Now we proceed to complete the square:
f(x) = - (4 · x² + 16 · x - 20)
- f(x) = 4 · x² + 16 · x - 20
- f(x) = (2 · x)² + 8 · (2 · x) - 20
- f(x) + 36 = (2 · x)² + 8 · (2 · x) + 16
- f(x) + 36 = (2 · x + 4)²
- f(x) + 36 = 4 · (x + 2)²
f(x) - 36 = - 4 · (x + 2)²
The vertex of the graph is (h, k) = (- 2, 36).
To learn more on quadratic equations: brainly.com/question/17177510
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