Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.
Write the function in standard form.
f(x) = 5x2 + 40x
Factor a out of the first two terms.
1(x) = 5(x2 + 8x)
Form a perfect square trinomial.
(%) =16
1(x) = 5(x2 + 8x + 16) -5(16)
What is the function written in vertex form?
® f(x) = 5(x + 4) -80
® f(x) = 5(x + 8) - 80
O f(x) = 5(x + 4)2 - 80
• f(x) = 5(x + 8) - 80

Sagot :

Answer: Choice C  [tex]f(x) = 5(x+4)^2 - 80[/tex]

======================================================

Reason:

The expression [tex]x^2+8x+16[/tex] factors to [tex](x+4)^2[/tex] using the perfect square trinomial formula [tex](a+b)^2 = a^2 + 2ab + b^2[/tex]. In this case, a = x and b = 4.

The -5(16) simplifies to -80

Therefore, [tex]5(x^2+8x+16) - 5(16)[/tex] turns into [tex]5(x+4)^2 - 80[/tex]

Compare this to [tex]a(x-h)^2 + k[/tex] to see that h = -4 and k = -80. The vertex is located at (h,k) = (-4, -80)

Answer:

c) 5(x+4)² - 80

Step-by-step explanation:

You have already gotten the third (second-last) step for finding the vertex as follows:

f(x) = 5(x² + 8x + 16) -5(16)

= 5(x+4)² - 80

Additional remarks: to find the vertex, you can just use find the value of x when x+4 = 0, meaning x = -4 and y = -80. Hence, the vertex is (-4, -80).

Hope this helps and feel free to mark this as brainliest! :)

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.