Key to "A quadratic function f is given f(x)=3x2+6x+4 a)..."

High School
Geometry
High school geometry
Transformation properties

Zain Padilla

Answered question

2022-02-14

A quadratic function f is given

f (x) = 3 x^{2} + 6 x + 4

a) Express f in transformation form

Answer & Explanation

iluvyou23452nwj

Beginner2022-02-15Added 19 answers

Step 1
We may quickly graph the given function by filling in the square.
a) $f (x) = 3 x^{2} + 6 x + 4$
f in transformation form is
$f (x) = 3 x^{2} + 6 x + 3 + 1$
$f (x) = 3 (x^{2} + 2 x + 1) + 1$
$f (x) = 3 {(x + 1)}^{2} + 1$
$f (x) = 3 {(x + 1)}^{2} + 1$
$y = 3 {(x + 1)}^{2} + 1$
$(y - 1) = 3 {(x + 1)}^{2}$
This is the common parabola equation with a vector (-1, 1)

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