1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
padilas [110]
3 years ago
10

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 bx c, is shown.step 1: –c = ax2 bxwhich b

est explains or justifies step 1?a.subtraction property of equalityb.completing the squarec.factoring out the constantd.zero property of multiplication
Mathematics
2 answers:
Ksju [112]3 years ago
3 0

Answer:

option (b) is correct.

First step to solve for deriving the quadratic formula from the quadratic equation is completing the square.

Step-by-step explanation:

Given : the quadratic equation ax^2+bx+c=0

We have to find the first step for deriving the quadratic formula from the quadratic equation.

Quadratic formula  is given by \frac{-b\pm\sqrt{b^2-4ac}}{2a}

Consider the given quadratic equation ax^2+bx+c=0

Divide the equation by a, we get,

x^2+\frac{b}{a}x+\frac{c}{a}=0

Take \frac{c}{a} to other side, we get,

x^2+\frac{b}{a}x=-\frac{c}{a}

Add (\frac{b}{2a})^2 to both side, we get,

x^2+\frac{b}{a}x+(\frac{b}{2a})^2=(\frac{b}{2a})^2-\frac{c}{a}

Thus, the left side is in the form of (a+b)^2=a^2+b^2+2ab

On solving, we get,

(x+\frac{b}{2a})^2=(\frac{b}{2a})^2-\frac{c}{a}

Then solve for x , we get quadratic formula \frac{-b\pm\sqrt{b^2-4ac}}{2a}

Thus, first step to solve for deriving the quadratic formula from the quadratic equation is completing the square.

Thus, option (b) is correct.

Yuliya22 [10]3 years ago
3 0
In deriving the quadratic formula from the equation 0=ax^2+bx+c where the first step is -c=ax^2+bx, subtraction property of equality best justifies step one. It states that when you subtract the same number in both sides of the equation, the expressions on both sides remain equal. In this case, we subtracted c from both sides resulting to the equation <span>-c=ax^2+bx.</span>
You might be interested in
Solve the equation.<br><br> x+4=−14<br><br> what does x equal
lisabon 2012 [21]
You just have to subtract four from each side to get x alone.
The answer is x = -18
8 0
3 years ago
Two cars leave from the same point at the same time, one traveling east and the other traveling west.
Citrus2011 [14]
Car travelling to the east is at 104 miles per hour and the car travelling to the west is moving at 114 miles per hour
8 0
3 years ago
PLEASE HELP !!! - after tip you gave a total of $321.75. If the original price of the meal was $300, what percent tip was applie
yan [13]

Answer: 7.25%

Step-by-step explanation:

There are a few ways to do this, but the easiest might be to set up a proportion:

321.75/300 = x percent/100 percent

Now cross multiply;

300x = 321.75(100) = 32,175

Divide both sides by 300 to solve for x:

300x/300 = 32,175/300

x = 107.25 This means that the tip was 7.25% on top of the $300 meal.

8 0
3 years ago
Read 2 more answers
Identify the vertex<br><br> y= —(x — 6)^2 + 2
alisha [4.7K]
(6,2)


Mark brainliest please

Hope this helps you
8 0
3 years ago
Convert y =(x+1)(x-9) to vertex form
IgorC [24]

Answer:

y = (x - 4)² - 25

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square.

Given

y = (x + 1)(x - 9) ← expand factors using FOIL, thus

y = x² - 8x - 9

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 8x

y = x² + 2(- 4)x + 16 - 16 - 9

  = (x - 4)² - 25 ← in vertex form

5 0
3 years ago
Other questions:
  • An amusement park charges $20 to enter the
    15·1 answer
  • What is the coefficient in the algebraic expression 7XY squared ?
    13·1 answer
  • Write the equation in slope- intercept form of the line that has a slope of -3 and contains the point (1,1)
    9·1 answer
  • Write a word problem for 1/5 divided by 10.
    8·2 answers
  • If you invest $823 at an interest rate of 3% how much money will you have after nine years
    6·1 answer
  • If i have 36 gallons in 4 minutes how many gallons per minute
    13·2 answers
  • #18-7: Find the radius of a circle that has an area of 4.5216 cm^2. Use 3.14 for pi.
    10·1 answer
  • You are playing a game and take the following turns first turn you earn 3 one point shots second turn you lose 2 two point shots
    12·1 answer
  • Solve. -3 + 9x = 24 (quick)
    5·2 answers
  • A circular base cone has base area of 28 whole number 2/7 cm² and a slant height of 5 cm. Calculate
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!