Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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

y = x^2 - 4x + 7​


Sagot :

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

[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]