Question

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?

f(x) = x2 + 36x + 12
f(x) = x2 – 36x – 12
f(x) = –x2 + 12x + 36
f(x) = –x2 – 12x – 36

Answer 1

f(x) = -x^2 - 12x - 36

Reason: -x^2 - 12x - 36 = -(x^2 + 12x + 36) = -(x + 6)^2, so x = -6 is a double root (the parabola touches but does not cross the x-axis).