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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]

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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! :)

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