FrostGDidn
Answered

Discover new perspectives and gain insights with IDNLearn.com's diverse answers. Our platform provides prompt, accurate answers from experts ready to assist you with any question you may have.

(Marking Brainliest) What is the vertex form of the equation?

y = x^2 - 4x + 7​

Sagot :

Reinhard10158idn

Step-by-step explanation:

y = x² - 4x + 7

the general vertex form is

y = m(x-h)² + k

to bring the part "x² -4x" to an expression of (ax + b)² we need to add 4, as "x² - 4x + 4" = (x - 2)².

and since we add 4 there, we need to subtract 4 overall again to keep the value of the expression the same :

y = x² - 4x + 4 + 7 - 4 = (x - 2)² + 7 - 4 = (x - 2)² + 3

and so, that is the vertex form :

y = (x - 2)² + 3

DᴀʀᴋPᴀʀᴀᴅᴏxidn

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's write the given equation into its vertex form ~

[tex]\qquad \sf  \dashrightarrow \: y = {x}^{2} - 4x + 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = {x}^{2} - 4x + 4 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = {x}^{2} - 2x - 2x + 4 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = {x(}^{} x - 2) - 2(x - 2) + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = (x - 2)(x - 2) + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = (x - 2) {}^{2} + 3[/tex]

Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.