Question

Graph $y=2{(x+1)}^2-3$using transformations

Short answer

The graph of$y=2{(x+1)}^2-3$is

Step-by-step solution

Step 1. Given data

The given function is

$y=2{(x+1)}^2-3$

Step 2. Plot the parent function 

Parent function of$y=2{(x+1)}^2-3$is $y=x^2$

Plot the graph of the $y=x^2$

Step 3. Horizontal shift

Plot $y={(x+1)}^2$by shifting the graph of $y=x^2$to left by one unit

Step 4. The vertical stretch  of the graph

Ploy the graph of$y=2{(x+1)}^2$stretching the graph of$y={(x+1)}^2$by the factor of$2$

Step 5. Vertical shift

Plot $y=2{(x+1)}^2-3$by shifting the graph of$y=2{(x+1)}^2$downward by $3$units