How do you write y=3(x−1)2+5 in standard form?

2 Answers
smendyka
Jul 25, 2017

See a solution process below:

Explanation:

First, we need to expand the squared term using this rule:

(a−b)2=a2−2ab+b2

Substituting x for a and 1 for b gives:

y=3(x−1)2+5

y=3(x2−[2⋅x⋅1]+12)+5

y=3(x2−2x+1)+5

Next, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

y=3(x2−2x+1)+5

y=(3×x2)−(3×2x)+(3×1)+5

y=3x2−6x+3+5

Now, combine like terms:

y=3x2−6x+(3+5)

y=3x2−6x+8

Nghi N
Jul 25, 2017

y=3x2+6x+8

Explanation:

y=3(x−1)2+5.
To convert the vertex form to standard form, we develop the vertex form:
y=3(x2−2x+1)+5=3x2−6x+3+5
y=3x2−6x+8

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