Question

How is the graph of the parent function y=x^2 transformed to produce the graph of y=3(x+1)^2?

Answer 1

Answer:

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

Step-by-step explanation:

We are given that a parent function

$y=x^2$

After transformation, we get a graph $y=3(x+1)^2$

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

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

$f(x)\rightarrow f(x+1)$

By applying this rule then, we get

$y(x)=(x+1)^2$

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

$f(x)\rightarrow 3f(x)$

Apply this rule then, we get

$y(x)=3(x+1)^2$

Answer 2

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.