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Ivahew [28]
2 years ago
11

Descried how to derive the quadratic formula from a quadratic equation in standard form

Mathematics
1 answer:
Aleks [24]2 years ago
8 0

Answer:

The standard form of a quadratic equation is:

ax^2+bx+c=0, a\neq 0

Quadratic Formula Derivation:

ax^2+bx+c=0\\

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

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

Completing the Square:

$x^2+\frac{b}{a}x +\frac{b^2}{4a^2} = \frac{b^2}{4a^2}-\frac{c}{a}$

$  ( x+\frac{b}{2a} )^2 =  \frac{b^2-4ac}{4a^2}  $

Square Root property:

$x+\frac{b}{2a}  = \pm \sqrt{ \frac{b^2-4ac}{4a^2}}   $

$x  = -\frac{b}{2a} \pm  { \frac{\sqrt {b^2-4ac}}{2a}}   $

$x  =  \frac{-b\pm\sqrt{b^2-4ac}} {2a}  }   $

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Y= - 2x + 4<br> 2x + y = 4
Tomtit [17]

Answer:

Infinite amount of solutions

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Terms/Coefficients
  • Coordinates (x, y)
  • Solving systems of equations using substitution/elimination

Step-by-step explanation:

<u>Step 1: Define Systems</u>

y = -2x + 4

2x + y = 4

<u>Step 2: Solve for </u><em><u>x</u></em>

<em>Substitution</em>

  1. Substitute in <em>y</em>:                                                                                                  2x + (-2x + 4) = 4
  2. Combine like terms:                                                                                         4 = 4

Here we see that 4 does indeed equal 4.

∴ the systems of equations has an infinite amount of solutions.

7 0
2 years ago
Read 2 more answers
(MULTIPLE CHOICE QUESTION)
weeeeeb [17]

Answer:

Transitive property is used in step 4.

Step-by-step explanation:

Transitive property states that if

a = b \\b = c\\ then\\a = c

Here we have

\angle 5 \cong \angle 1\\\angle 1 \cong \angle 3\\then\\\angle 3 \cong \angle 5

3 0
2 years ago
Read 2 more answers
The volume of sphere Q is 50% more than the volume of sphere P. The volume of sphere R is 50% more than the volume of sphere Q.
STALIN [3.7K]
<h2>Use this link to find your answer</h2><h2>http://ldh.la.gov/</h2>
6 0
3 years ago
2x=90<br> 3y-2x=90<br> Please tell me work
svp [43]
90 divided by 2= 45 so x=45
2•45=90
So, for the next one y=60 because 90+90=180
3•60-2•45=90
5 0
3 years ago
Not really getting this can someone plz explain.
Komok [63]

your answer would be b becuase that is 3/6 so thats half and ou would simply it and 1/4 do the same

7 0
2 years ago
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