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

  f(x) = –x^2 – 12x – 36

Step-by-step explanation:

The parent function, x^2, touches the x-axis at x=0. Translating it 6 units left replaces x with x-(-6) = x+6, so the function is ...

  f(x) = (x+6)^2 = x^2 +12x +36

Reflecting the graph across the x-axis doesn't change the x-intercept, so Heather could be writing ...

  f(x) = -x^2 -12x -36

the answer is b

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step-by-step explanation: