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Mrrafil [7]
3 years ago
5

PLEASE HELP!! Compare & Contrast how Completing the Square is used to Convert a quadratic function to vertex form with how i

t is used to Solve a quadratic equation.
Mathematics
1 answer:
Likurg_2 [28]3 years ago
7 0

Answer:

Step-by-step explanation:

Given a general quadratic formula given as ax²bx+c = 0

To generate the general formula to solve the quadratic equation, we can use the completing the square method as shown;

Step 1:

Bringing c to the other side

ax²+bx = -c

Dividing through by coefficient of x² which is 'a' will give:

x²+(b/a)x = -c/a

- Completing the square at the left hand side of the equation by adding the square of half the coefficient x i.e (b/2a)² and adding it to both sides of the equation we have:

x²+(b/a)x+(b/2a)² = -c/a+(b/2a)²

(x+b/2a)² = -c/a+(b/2a)²

(x+b/2a)² = -c/a + b²/4a²

- Taking the square root of both sides

√(x+b/2a)² = ±√-c/a + b²/√4a²

x+b/2a = ±√(-4ac+b²)/√4a²

x+b/2a =±√b²-4ac/2a

- Taking b/2a to the other side

x = -b/2a±√√b²-4ac/2a

Taking the LCM:

x = {-b±√b²-4ac}/2a

This gives the vertex form with how it is used to Solve a quadratic equation.

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Juan’s age is 5 years more than twice Margo’s age. The sum of their ages is 29 years. Find their ages
Brut [27]

x Margo's age

Jaun + Margo

(2x+5) + x = 29

3x = 24

x = 8, Margo's age. Jaun 21 2*8+5

And to check...

sum = 29


5 0
3 years ago
Which equations support the fact that rational numbers are closed under subtraction?
Illusion [34]

Answer:

A rational number is said to be closed if the subtracted values and the result obtained are rational. Hence, the equations which supports the condition are :

5.5 - 0.5 = 4

5√4 - √4 = 4√4

Step-by-step explanation:

A.)

√8 - √8 = 0 ; the added values aren't rational and the result, Zero is not rational either.

B.)

5√4 - √4 = 4√4

5(2) - 2 = 2(2)

10 - 2 = 4

All the values in the expression are rational ; hence, it supports the assertion.

C)

5.5 - 0.5 = 4 ; all the values in the expression are rational, hence, it supports the fact.

2√3 - √3 = √3 ; the values in the expression are not rational, hence, it does not meet the condition.

Therefore, only options B and C supports the assertion.

Let me add that I learned most of this from Brainly a user named fichoh :)

7 0
2 years ago
Three times the difference of eight and twice a number is five times the number.
Softa [21]

Answer:

24

Step-by-step explanation:

3(2n-8)=5n distribute 3

6n-24=5n combine like terms

-24=-n divide by -1 on both sides

24=n

n=24

7 0
3 years ago
There are 365 days in a year and 24 hours in a day. An airport camera records for 18 hours and then automatically resets itself
likoan [24]

The answer is 486.6

There are 8,760 hours in a year, so 18 divided by 8,760 would = 486.6

5 0
3 years ago
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The measure of angle JKL is 160.
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Answer:

x + 160° 95°=360°

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8 0
2 years ago
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