Question

How many times does the graph y = (x + 3)2 touch the x-axis?
x

Answer 1

Answer:

one

Step-by-step explanation:

y = (x + 3)^2

Start with the parent function y = x^2.

y = x^2 touches the x-axis at only 1 point, (0, 0).

The difference between y = (x + 3)^2 and its parent function y = x^2, is that in y = (x + 3)^2, x was replaced by x + 3. That is a translation of 3 units left. The function y = (x + 3)^2 still only touches the x-axis once, but at x = -3.

Answer: one

Answer 2

Answer:

Step-by-step explanation:

To answer this, set the function y = (x + 3)^2 touch the x-axis (where y = 0) and find the actual value(s) of x:

y = (x + 3)^2 = 0

Taking the square root of both sides, we get x + 3 = ±0, or x = -3.  As this equation is a quadratic, there MUST be two roots; the roots are {-3, -3}.  Thus in theory, the graph touches the x-axis in two places, but these two places are identical:   (-3, 0)