Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing?

A parabola that touches the x-axis at x = −6 has a double root there, so its function must have the form a(x + 6)² for some nonzero number a. Choice D is −x² − 12x − 36 = −(x + 6)², which equals zero at x = −6 and does not cross the x-axis.

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