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Vika [28.1K]
3 years ago
10

Complete the square to find the minimum value of the expression 4x2 + 8x + 23.

Mathematics
1 answer:
Tcecarenko [31]3 years ago
3 0
So you need to come up with a perfect square that works for the x coefficients.
like.. (2x + 2)^2
(2x+2)(2x+2) = 4x^2 + 8x + 4
Compare this to the equation given. Our perfect square has +4 instead of +23. The difference is: 23 - 4 = 19

I'm going to assume the given equation equals zero..

So, If we add subtract 19 from both sides of the equation we get the perfect square.

4x^2 + 8x + 23 - 19 = 0 - 19
4x^2 + 8x + 4 = - 19
complete the square and move 19 over..
(2x+2)^2 + 19 = 0
factor the 2 out becomes 2^2 = 4
ANSWER: 4(x+1)^2 + 19 = 0

for a short cut, the standard equation
ax^2 + bx + c = 0 becomes a(x - h)^2 + k = 0
Where "a, b, c" are the same and ..
h = -b/(2a)
k = c - b^2/(4a)

Vertex = (h, k)
this will be a minimum point when "a" is positive upward facing parabola and a maximum point when "a" is negative downward facing parabola.


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Is there answer choices
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Can anyone solve 9, 10, 11, 12, and 13 I'm stuck on those problems, I already solved 14, 15, and 16 on paper.
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Answer:

9. x>-4 or x≥1

10. a<2 or a≥-5

11. v≤7 or v≥-4

12. k≥5 or k<8

13. n>6.8 and n≤9

Step-by-step explanation:

9. -2x-7>1

-2x>8

x>-4

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10.a/-2 <-1

a<2

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11. 6v+38≤-4

6v≤-42

v≤7

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12. 4(1-k)≥-16

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45<br> as a product of prime factors
Darya [45]
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:)
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Which answer choice shows 4 + 0.3 + 0.09 written in standard form?
puteri [66]

Solution:

<u>A few changes were made:</u>

  • 4 as 4.00.
  • 0.3 as 0.30

<u>New equation:</u>

  • 4 + 0.3 + 0.09 = 4.00 + 0.30 + 0.09

<u>Solving the equation:</u>

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Correct option is B.

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