Question

quadratic functions: standard form

what is the range of the function (f(x) = 3x^2 + 6x - 8)?

options:
\\(\\{y \mid y \ge -1\\}\\)
\\(\\{y \mid y \ge -11\\}\\)
\\(\\{y \mid y \le -11\\}\\)

Explanation:

Identify the quadratic coefficients

Using the Quadratic Functions knowledge point

$$
LATEXBLOCK0
$$

Find the x-coordinate of the vertex

Using the Vertex of Quadratic Function knowledge point

$$
LATEXBLOCK1
$$

Find the y-coordinate of the vertex

Using the Vertex of Quadratic Function knowledge point

$$
LATEXBLOCK2
$$

Determine the range of the function

Using the Domain and Range knowledge point

$$
LATEXBLOCK3
$$

Answer:

• {y | y \(\ge\) -1}
• {y | y \(\ge\) -11} (Correct answer)
• {y | y \(\le\) -11}
• {y | y \(\le\) -1}