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

User Binard
by
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2 Answers

22 votes
22 votes

Answer:

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)

User SuperAadi
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2.6k points
25 votes
25 votes

Answer:

one

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

User Nishchay Sharma
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2.6k points