Respuesta :

musiclover10045

The +1 in parenthesis is adding one to the x value, which shifts the graph 1 unit to the left, called a horizontal translation.

The 3 outside of the parenthesis is multiplying the X value by 3, which narrows the shape of the graph ( makes the curve 3 times sharper), which is called a vertical stretch.

lublana

Answer:

Shift 1 units towards left and then stretch vertically 3 times.

Step-by-step explanation:

We are given that a parent function

[tex]y=x^2[/tex]

After transformation, we get a graph [tex]y=3(x+1)^2[/tex]

We have to find that how the parent function transformed to produce the graph of [tex]y=3(x+1)^2[/tex]

The parent graph is shifted  1 unit towards left by the rule of transformation

[tex]f(x)\rightarrow f(x+1)[/tex]

By applying this rule then, we get

[tex]y(x)=(x+1)^2[/tex]

Now, the parent function stretched vertically 3 times the previous graph  by the rule

[tex]f(x)\rightarrow 3f(x)[/tex]

Apply this rule then, we get

[tex]y(x)=3(x+1)^2[/tex]

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