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
TiliK225 [7]
3 years ago
11

What is the vertex form of the equation?

Mathematics
2 answers:
GuDViN [60]3 years ago
7 0
We need to write the equation in its vertex form so we have to know the general equation for the vertex form. It is written as:

y = (x - h)^2 + k

where h and k represents the point of the vertex.

We go as follows:

y = (x^2 + 4x) – 3 
y +4= (x^2 + 4x+4) – 3 
y = (x + 2)^2 - 7

Therefore, the correct answer from the choices is option B.
leva [86]3 years ago
4 0

The vertex form of the equation x^{2}+4x-3 is \fbox{\begin{minispace}\\ \math (x+2)^{2} -7\end{minispace}}, that is \fbox{\begin{minispace}\\option B\end{minispace}}.

Step-by-step explanation:

A quadratic equation is a two degree equation that has the standard form ax^{2}+bx+c.

The degree of the given equation x^{2}+4x-3 is 2 therefore it is a quadratic equation.

Every quadratic equation represents a parabola so the given equation also represents a parabolic function.

The standard form of equation of a parabola is written as shown below.

\fbox{\begin{minispace}\\ \math a(x-h)^{2}+k\end{minispace}}

Here, the value of a represents whether the parabola is upwards or downward and the point (h,k) is the vertex of the parabola.

Therefore, the above equation form is known as the vertex form of the equation.

To transform any quadratic equation into its vertex form, we use completing the square method.

Firstly, if the coefficient of x^{2} is other than 1 then divide the complete equation by that coefficient.

Here, the coefficient of x^{2} is 1 so the first step is not required.

Now, add a value and subtract the same value such that it forms a perfect square.

For a standard quadratic equation ax^{2}+bx+c, the value that is added and subtracted in the expression is calculated as \left(\dfrac{b}{2a}\right)^{2}.

Hence, add and subtract 4 to the equation and simplify as shown below.

\begin{aligned}x^{2}+4x-3&=x^{2}+4x-3+4-4\\&=x^{2}+4x+4-3-4\\&=(x+2)^{2}-7\end{aligned}

Therefore, the vertex form of the equation x^{2}+4x-3 is \fbox{\begin{minispace}\\ \math (x+2)^{2} -7\end{minispace}}.

Learn more:

1. General form of equation of a circle brainly.com/question/1506955

2. Domain and range of a function brainly.com/question/3412497

3. Coordinate geometry brainly.com/question/7437053

Answer details

Grade: Middle school

Subject: Mathematics  

Chapter: Quadratic equation

Keywords: equation, vertex form, quadratic equation, parabola, vertex, coefficients, add, subtract, divide, standard form, simplify, completing the square, vertex point, degree.

You might be interested in
This answer needs to be rounded to the nearest hundredth. Example:12.34
lara [203]
Answer is 14.14
Reason
Using Pythagorean theory
a^2 + b^2 = c^2
The two legs are a and b, the longest diagonal opposite the right angle is c
10^2 + 10^2 = c^2
200 = c^2
Take square root of both sides
14.14 = c
7 0
1 year ago
two patterns start at 0. the rule for pattern A is add 2. the rule for pattern B is add 3. what is the value of pattern B when p
mariarad [96]

Answer:4.5

Step-by-step explanation:

A   0   1       2      3

B   0   1.5    3     4.5

7 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20-%205%282y%20-%208%29%20-%203%281%20%2B%20x%29%20-%207" id="TexFormula1" title=" - 5(2y - 8
Andre45 [30]
-(2y-8)-3(1+x)-7
-10y+40-3(1-x)-7
-10y+40-3-3x-7
-10y+30-3x
5 0
3 years ago
Read 2 more answers
HELP HELP PLEASE I NEED HELP
dimaraw [331]

Answer:

<h2>FALSE</h2>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • PEMDAS
<h3>tips and formulas:</h3>

order of PEMDAS

  1. parentheses
  2. exponent
  3. multiplication or
  4. division
  5. addition
  6. subtraction
  • left to right
<h3>let's solve:</h3><h2><u>L.</u><u>H.S</u><u>=</u></h2>
  1. <u>\sf simplify  \: divition:  \\  \tt 14 + 33 + 0.4</u>
  2. <u>\sf simplify \: additio n :  \\  \tt 47.4</u>
<h2><u>≠R.H.S</u></h2>

therefore

<h3>the equality is false</h3>

8 0
3 years ago
HURRY PLZ
Oliga [24]

Answer:

6x + 2(−2x + 1) = 22

Step-by-step explanation:

6x + 2(−2x + 1) = 22

This step can be used to solve by substitution method.

8 0
3 years ago
Other questions:
  • Han spent 75 minutes practicing the piano over the weekend priya practiced the Villon 152% as much time as han practiced the pia
    5·2 answers
  • There are 40 boys in the club. the ratio of girls to boys is 2 to 5. how many girls are in the club
    9·1 answer
  • Is -6 a real, complex, pure imaginary or nonreal complex
    8·2 answers
  • Write an equation of the circle with center (-5,2) and radius 4.
    10·1 answer
  • NEED ANSWER ASAP. WILL MARK THE BRAINLIEST
    9·2 answers
  • Which mathematical inequality represents the following statement?
    15·1 answer
  • Debby used a garden hose to fill up a 4-gallon bucket in just 1/6 of a minute. At what rate does water flow through the hose?​
    8·1 answer
  • SUMMARY: how can you use mapping rules to find rotations of objects at 90, 180, and 270 degrees?
    12·1 answer
  • Triangle △A′B′C′ is the image of △ABC under a dilation with a scale factor of 2.
    5·1 answer
  • Work out the missing value in the estimation below.<br> 237 + 462 ~ 200 +
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!