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a_sh-v [17]
3 years ago
15

Rewrite the function by completing the square f(x) =4x2+12x+9

Mathematics
1 answer:
Ilya [14]3 years ago
7 0

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = 4x² + 12x + 9

The coefficient of the x² term must be 1 so factor out 4 from the first 2 terms

f(x) = 4(x² + 3x) + 9

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 3x

f(x) = 4(x² + 2(\frac{3}{2})x + \frac{9}{4} - \frac{9}{4}) + 9

     = 4(x + \frac{3}{2})² - 9 + 9

     = 4(x + \frac{3}{2})²

Thus

f(x) = 4x² + 12x + 9 = 4(x + \frac{3}{2})²

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The sum of two numbers is -9. The difference of the two numbers is -41. What are the two numbers?
Nataly [62]

Answer:

the two numbers are 16 and -25

Step-by-step explanation:

Let the two numbers be x and y

x+y=-9

x-y=-41

By substitution

y=-9-x

x-(-9-x)=-41

x+9+x=-41

2x=-41-9

2x=-50

x=-25

y=-9-(-25)

y=16

6 0
3 years ago
Can someone please help me on this question?​
yan [13]

Answer: q³⁰

Explanation:

First just solve the first part using the exponent rules

p²q⁵ becomes 1/p-⁸q-²⁰ then we flip the fraction so the exponents become positive. Now we have p⁸q²⁰.

Before multiplying the other equation, we must simplify. p-⁴q⁵ becomes 1/p⁴q-⁵ and since it's the exponents being raised to a power we simply multiply the inner exponents times the outer exponent which yields 1/p⁸q-¹⁰. We must make q-¹⁰ positive so we will then bring it to the numerator of the fraction which gives us: q¹⁰/p⁸.

Multiply q¹⁰/p⁸ * p⁸q²⁰/1 = p⁸q³⁰/p⁸ divide the p exponents by each other which yields 0 since when u divide exponents you just subtract them so 8 - 8 = 0. Your answer is now q³⁰/1 or just q³⁰

4 0
3 years ago
Divide by long division method 4x³-x+1by(2x-1)
katen-ka-za [31]
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totally answer.
4 0
3 years ago
Which function forms an arithmetic sequence when x = 1,2,3,…?<br> ( help please! )
MariettaO [177]

Step-by-step explanation:

hope you can understand

3 0
2 years ago
Use the drawing tool(s) to form the correct answers on the provided graph.
DENIUS [597]

Answer:

I think x = 1 but I’m not sure I’m sorry

Step-by-step explanation:

3 0
3 years ago
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