Question

What is the range of the function f(x) = 3x2 + 6x - 8?

Answer 1

Answer:

  {y | y ≥ -11 }

Step-by-step explanation:

To answer a question like this, it is often helpful to graph the function or to rewrite it to vertex form.

  f(x) = 3x^2 +6x -8

  f(x) = 3(x^2 +2x) -8 . . . . factor the leading coefficient from x terms

  f(x) = 3(x^2 +2x +1) -8 -3(1) . . . . complete the square*

  f(x) = 3(x +1)^2 -11

The form of this equation tells you that the graph is a parabola that opens upward. Its vertex is (-1, -11), so the minimum value is -11. The range is the vertical extent of the function values, so goes upward from -11:

  y ≥ -11

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* Vertex form is ...

  f(x) = a(x -h)^2 +k

where "a" is the vertical scale factor and (h, k) is the vertex. When "a" is positive, the parabola opens upward; when it is negative, the parabola opens downward.

The square is completed by adding the square of half the x-coefficient inside parentheses, and subtracting the equivalent amount outside parentheses. Here, we had 2x inside parentheses, so we added (2/2)^2 = 1 inside and -3(1) outside, because "a" was 3.

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Brainly provides tools for properly rendering math symbols. 2-11 is not the same as ≥-11.