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Marina86 [1]
1 year ago
15

Find the vertex of the graph of f(x)=-4(x-1)(x+5)

Mathematics
1 answer:
madreJ [45]1 year ago
7 0

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

#SPJ1

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3 years ago
Complete the table of values for the equation y = 3x + 5.
cricket20 [7]

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3 0
2 years ago
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bagirrra123 [75]

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1) 20% change I think its an increase.

If needed I could try to answer the 2nd question but I am sure that I got the first one right.

Step-by-step explanation:

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3 years ago
What is the value of the geometric sequence for which a1=10 and r=0.5?
tiny-mole [99]
The formula for an infinite geometric sequence is the following:

S_{∞}= \frac{a_{1}}{1-r}

Just substitute the values of a_{1} and r into the formula.

S_{∞}=\frac{10}{1-0.5}
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Therefore, the answer is 20.
3 0
3 years ago
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zloy xaker [14]

Answer:

19. reflection (-1, -3)

20. translation (5, -3)

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22. reflection (1, 3)

23. translation (5, 6)

24. reflection (1, 3)

Step-by-step explanation:

4 0
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