how to know which way to solve a quadratic equation

Answers

Answer 1

Answer:

  Practice -- lots of it

Step-by-step explanation:

I usually choose a solution method that I believe will find the desired answer for me in the least number of simple steps. What constitutes a "simple" step depends on a number of things:

the given information and/or the given form of the equationfamiliarity with all of the different solution processesfamiliarity with arithmetic facts (multiplication tables, squares)familiarity with quadratic forms: difference of squares, perfect square binomials, product of binomials, vertex formavailability of a graphing calculatorwhether an approximation will serve the purpose.

__

I often choose a graphing calculator as my first approach to solving a quadratic. It easily shows the roots, and can show the vertex. (Sometimes, scaling the graph is required, so I actually prefer to use a touch-screen for the purpose. It is easier to "pinch" than to type in possible graph limits by trial and error.) The answer is generally provided to 3 or 4 significant figures, which is usually enough to tell if the solution is rational or irrational.

The easiest way to describe an integer (or rational) solution to someone else (on Brainly, for example) is usually to show the factoring of the quadratic. Finding the roots with a graphing calculator significantly aids the factoring process. (It is much easier to "find" the solution if you know the solution before you start looking.)

__

As we said at the beginning, the answer to your question is "practice." Many curricula try to offer opportunities to practice. I find most of these pretty annoying. What I suggest is that you find your own internal motivation to practice solving different kinds of quadratics in several different ways. That is, solve the same quadratic by ...

using the formulacompleting the squarefactoringgraphing (with a graphing calculator)scaling and/or translation and/or transformation*

It might take you a couple of hours of work to learn the best way to solve an equation in under 5 minutes.

In this process, you will discover what you need to know to choose a method that works nicely for you. I believe you will find that total familiarity with arithmetic facts (sums, products, squares) and operations on all the different ways to represent numbers (integer, decimal, fraction, percent, scientific notation) will help you significantly.

_____

* Additional comment

Some "area" problems give you the difference of dimensions (length and width), and ask you to find the dimensions that give a specific area. This can be solved by (x)(x -d) = A. If you don't immediately recognize factors of A that differ by d, then you might have to resort to the quadratic formula to solve this.

Another approach is to let the variable represent the average dimension. Then the equation becomes (x -d/2)(x +d/2) = A, which is a "difference of squares" form that is much more easily solved. The solution for x is √(A +(d/2)²), and all you have to do is add and subtract d/2 from that solution to find the dimensions. This is an example of what I mean by transforming the problem.


Related Questions

what's 1+1 ???

enjoy!

Answers

1+1= -2628474
hope it helps

Use the linear combination method to solve the system of equations. â€""3x 8y = 16 3x 4y = 8 What is the value of x? â€""1 0 1 2.

Answers

The value of x from the system of equation is 0

Given the systems of equation

–3x + 8y = 16

3x + 4y = 8

Using the elimination method.

Add both equations

-3x + 3x + 8y + 4y = 16 + 8

12y = 24

y = 24/12

y = 2

Substitute y = 2 into equation 2:

3x + 4y = 8

3x + 4(2) = 8

3x = 8 - 8

3x = 0

x = 0

Hence the value of x from the system of equation is 0.

Learn more on simultaneous equations here:https://brainly.com/question/185757

A typical tip at a restaurant is 18% of the total bill. If the bill is $60, what would the typical tip be?

The typical tip would be $_________.

Answers

The typical tip would be $10.80
It will be 24.15 I think

1 4/8 in a improper fraction?

Answers

Answer:[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Step 1: Multiply the whole number part (1) by the denominator (8).

1 × 8 = 8

Step 2: Add the product from Step 1 (8) to the numerator (4).

8 + 4 = 12

Step 3: Write that result (12) above the denominator. So,

[tex]\frac4{8}{1}[/tex]

Step 4: The fraction [tex]\frac{12}{8}[/tex]

Can be reduced by dividing both numerator and denominator by the GCD(12,8) = 4. Thus,

[tex]\frac1{4}{8} =\frac{3}{2}[/tex]

(03.02) If g(x) = x2 + 2, find g(3). (2 points) Group of answer choices 9 8 11 6

Answers

this answers is 8 am I right

468 divided by 3 step by step solution

Answers

Answer:

156

Step-by-step explanation:

468 ÷ 3

= 156

hope u liked the answer :)

#keep learning

Find the HCF of x 2 y 3 and x 3 y

Answers

Answer:

the answer is to the question is x2×y×3

Select “Rational” or “Irrational” to classify each number.

Answers

1. rational 2. irrational 3. irrational 4. rational

Which number line correctly shows 4.5 – 2.5?
a) A number line going from 0 to 4.5 in increments of 0.5. An arrow goes from 0 to 4.5 and then backwards from 4.5 to 2.
b) A number line going from negative 4.5 to 0 in increments of 0.5. An arrow goes from negative 4.5 to negative 2 and then backwards from 0 to negative 4.5.
c) A number line going from negative 2.5 to positive 4.5 in increments of 0.5. An arrow goes from negative 2.5 to 0 and also from 0 to 4.5.
d) A number line going from negative 4.5 to positive 2.5 in increments of 0.5. An arrow goes from 2.5 to 0 and from 0 to negative 4.5.

Answers

Answer:

its A i think

Step-by-step explanation:

Hope this helps!

Gas grills are on sale 20% off. The sale price of the grill that I like is $399.20. What was the original price of the grill?

Answers

Answer:

499

Ste-by-step explanation

80 percent of the original price is left.

If you divide by 4 you get 99.8 which is 20% of the original price. Then if you multiply 99.8 by 5 you will get 100% of the original price which is 499

You can also do 399.2 * 1.25 = 499

Francisco sold 9 rolls of wrapping paper for a band fundraiser earning the band $22.50. Sharon sold 16 rolls of wrapping paper and earned $40.00 for the band. If this relationship is graphed with the number of rolls sold on the x-axis and the money earned on the y-axis, what is the slope of the graph in dollars per roll?

A. 1.25
B. 2.50
C. 3.75
D. 5.00

Answers

Answer:

A

Step-by-step explanation:

If  the relationship is graphed with the number of rolls sold on the x-axis and the money earned on the y-axis

Then the two points on that line will be (14,17.50) and (16,20)

We know that the slope of a lien with points  is give by:-

Hence, the slope of the graph with points  (14,17.50) and (16,20) is given by :-

Therefore, the slope of the graph = 1.25 dollars per roll.


Gary multiplied ab and ab' as shown below.
(a+b)(ab) - ab?
Is Gary's answer correct?

Answers

Answer: I believe he is wrong because when I had to do this it was (a+b)(a+b)-ab

You are selling candy for $2 each and burgers for $5 each. You have a budget for $150. The equation for this situation can be written as 2x+5y=150

Find the x intercept and y intercept. Show all work.

If you are selling 0 burgers, how many candies did you sell? Show your work.







If you are selling 0 burgers, how many candies did you sell? Show your work.



Answers

30 burgers because 5 x 30=$150

Prove that 4x-1 =11,in which the value of x=3​

Answers

Answer:

3

Step-by-step explanation:

substitute where x=3 into the equation

so 4*3-1=11

4×3-1=11

12-2=11

11=11

proved..

2th grade Student 1+1=11?!? my teacher told me that

Answers

Answer:

Not much sure if this is a joke but 1+1 is 2 not 11.

Step-by-step explanation:

I hope I helped.

Have a great day ;)

Julia went into a movie theater and bought 2 bags of popcorn and 5 pretzels, costing a total of $37.25. Zoe went into the same movie theater and bough 8 bags of popcorn and 9 pretzels, costing a total of $102.25. Write and solve a system of equations to determine the price of each bag of popcorn and the price of each pretzel.

Answers

Taking into account the definition of a system of linear equations, the price of each bag of popcorn is $8 and the price of each pretzel is $4.25.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

x: price of each bag of popcorn. y: the price of each pretzel.

On one hand, Julia went into a movie theater and bought 2 bags of popcorn and 5 pretzels, costing a total of $37.25.   This is expressed by 2x+5y= 37.25

Zoe went into the same movie theater and bough 8 bags of popcorn and 9 pretzels, costing a total of $102.25.  This is expressed by 8x+9y=102.25

So, the system of equations to solve is:

[tex]\left \{ {{2x+5y=37.25} \atop {8x+9y=102.25}} \right.[/tex]

There are various methods to solve a system of equations, it is decided to solve by the substitution method, which consists of solving one of the two variables in one of the equations of the system and substituting its value in the other equation.

So, isolating the variable x from the first equation:

2x+5y= 37.25

2x= 37.25 - 5y

x= (37.25 - 5y)÷2

x= 18.625 - [tex]\frac{5}{2}[/tex]y

Replacing in the second equation:

8×(18.625 - [tex]\frac{5}{2}[/tex]y)+9y=102.25

Solving:

8×18.625 - 8×[tex]\frac{5}{2}[/tex]y+9y=102.25

149 - 20y + 9y=102.25

149 -11y= 102.25

-11y= 102.25-149

-11y= -46.75

y= (-46.75)÷ (-11)

y= 4.25

Finally, replacing in x= 18.625 - [tex]\frac{5}{2}[/tex]y and solving you get:

x= 18.625 - [tex]\frac{5}{2}[/tex]×4.25

x= 18.625 - 10.625

x=8

Remembering that x represents the price of each bag of popcorn and y represents the price of each pretzel, you get that the price of each bag of popcorn is $8 and the price of each pretzel is $4.25.

Learn more about system of equations:

https://brainly.com/question/14706985?referrer=searchResults

https://brainly.com/question/14748961?referrer=searchResults

https://brainly.com/question/16763389

Select the four equivalent expressions to 4x^2 - 4x -24

A - 2x^2 - 2x - 12

B - 4(x^2 - x - 6)

C - 4(x - 3)(x + 2)

D - (2x - 2x)^2 - 24

E - (4x - 12)(x +2)

F - (x - 3)(4x + 8)

Answers

Answer:

b. 4(x^2 - x - 6)

c. 4(x - 3)(x + 2)

e. (4x - 12)(x +2)

f. (x - 3)(4x + 8)

hope it helps :)

mark brainliest!!

multiply the expression (1/3 m-n)^2​

Answers

Answer:

{(

Answer : 1/4 m^2 -mn + n^2

Evaluate the expression wx when x = -15 and w = 5. wx = _________.
-3 75 -75 3

Answers

w = -15 and x = 5
-15 x 5 is ur equation
15 x5 is 75 but the 15 is negative so its -75

Answer:

-75

Step-by-step explanation:

i had the exam so it is write

write the ratio as a fraction in simple form 14 boxes:8 boxes​

Answers

The ratio in its simplest form is 7:4

help pleasee
on the image
with the steps.​

Answers

Answer:

  an = 22 -6(n -1)

Step-by-step explanation:

The first term of the sequence is given as a1 = 22. The general term of an arithmetic sequence is ...

  an = a1 +d(n -1) . . . . n-th term for first term a1 and common difference d

The third term will be ...

  a3 = 10 = 22 +d(3 -1)

Then the common difference is ...

  10 -22 = 2d

  -12/2 = d = -6

__

Putting the known values into the formula for the general term, it becomes ...

  an = 22 -6(n -1)

__

This can be simplified to ...

  an = 28 -6n

if you can answer any of these that would be great !

Answers

Answer:

Step-by-step explanation:

number 2) 0

A money market account dropped to 5/8 its original value of $7.200. What is its current value?

A. 180
B. 450
C. 1,152
D. 4,500
E. 11,520

Answers

Answer:

Which claim most accurately describes the energy transformation taking place while he practices his guitar?

Sound energy is converted into elastic energy.

Kinetic energy is converted into thermal energy.

Mechanical energy is converted into sound energy.

Electrical energy is converted into mechanical energy.

Step-by-step explanation:

Answer:

C. 4,500

Step-by-step explanation:

Since we have 5/8 of the original 7200, we can multiply and divide.7200*5=3600036000÷8=4500Therefore, the answer is c, 4,500

please no links!!!!!!!!!!!

Suppose a trip is 355.1 miles long and you want to spend 2 days driving. How many miles
should you drive each day?

Answers

Answer: 177.55 miles

Step-by-step explanation: 355.1/2

                                            = 177.55 miles each day

Answer:

177.55mi/day

Step-by-step explanation:

If you travel for x number of days and want to split your trip evenly across those days, simply divide the distance you need to travel by the number of days.

What the vertex of y=4(x-3)^2+3

Answers

Answer:

(3,3)

Step-by-step explanation:

we rewrite in vertex form and use this form to find the vertex (h,k)

A bag has 25 beads in it.the probability of picking a white bead is 3/5.how many white beads are in the bag

Answers

I think the answer is 5
There are 15 white beads in the bag. (1/5 of 25 is 5.)

Write (5/3)³ as a quotient of powers.

Answers

Answer:

The number (5/3)³ written as a quotient of powers is; 5³/3³

According to the question;

We are required to determine write the number, (5/3)³ as a quotient of powers

The number (5/3)³ can be evaluated as;

= 125/27

= 5³/3³

Step-by-step explanation:

Help me solve this please!

Answers

Answer:

x=15

Step-by-step explanation:

if you put 8x-10=110 you can solve for x and get 15. this only works because they are opposite & congruent sides

I don’t know how to simplify this fully;15x/5xy

Answers

Answer:

3/y

Step-by-step explanation:

15x

5xy

you would divide top and bottom by 5x, since it is their only common divisor.

you would then get 3/y. hope this helps

WHO CAN HELP ME ON THIS? Due soon!

Answers

The other one will. Be 20
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