Check the solution to "y=12(x−4)2 Transformations"

Brittney Lord

Answered question

2020-12-21

y = \frac{1}{2} {(x - 4)}^{2}

Transformations

Answer & Explanation

pierretteA

Skilled2020-12-22Added 102 answers

The parent function of

y = \frac{1}{2} {(x - 4)}^{2}

so we need to determine what transformations must be done to

y = x^{2} \to \geq t y = \frac{1}{2} {(x - 4)}^{2} .

A transformation of the form g(x)=af(x) is a vertical stretch when ∣a∣>1, a vertical compression when ∣a∣<1, and a reflection across the x-axis when a<0.
For

y = \frac{1}{2} {(x - 4)}^{2}, a = \frac{1}{2}

. Since

\frac{1}{2}

is positive and smaller than 1, then there is no reflection and there is a vertical compression by a factor of

\frac{1}{2} .

A transformation of the form g(x)=f(x−h) is a horizonatal translation right hh units when h>0 and left ∣h∣∣ hits when h<0h
For

y = 12 {(x - 4)}^{2}, h = 4

. Since 4 is greater than 0, then the translation is right 4 units.
The transformations are then: vertical compression by

\frac{1}{2}

and a translation right 4 units.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Algebra I

Didn't find what you were looking for?