Which equation defines the graph of y = x² after it is shifted vertically 3 units down and horizontally 5 units left?
y=(k - 5)² - 3
y= (k + 5)² - 3
y=(k - 3)² - 5
y= (k + 3)² - 5

Solution:

Given, y = x²

We have to find the equation that defines the graph of y = x²

The parent equation is y = x²

The new equation is y = a(x - k)² + h

The graph is shifted vertically 3 units down

So, h = -3

The graph is shifted horizontally 5 units left

So, k = -5

Now, y = 1(k - (-5))² + (-3)

y = (k + 5)² - 3

Therefore, y = (k + 5)² - 3 defines the graph of y = x².

Which equation defines the graph of y = x² after it is shifted vertically 3 units down and horizontally 5 units left?

Summary:

The equation y = (k + 5)² - 3 defines the graph of y = x² after it is shifted vertically 3 units down and horizontally 5 units left.