Graph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing. $f\left(x\right)=3x^2+12x$

• A.
• B.
• C.
• D.

Answer: (C)

Verified step by step guidance

1. Identify the standard form of the quadratic function, which is f(x) = ax^2 + bx + c. In this case, f(x) = 3x^2 + 12x, where a = 3, b = 12, and c = 0.
2. Find the vertex of the parabola using the formula for the x-coordinate of the vertex, x = -b/(2a). Substitute a = 3 and b = 12 into the formula to find the x-coordinate.
3. Calculate the y-coordinate of the vertex by substituting the x-coordinate back into the function f(x). This gives you the vertex (h, k).
4. Determine the axis of symmetry, which is the vertical line that passes through the vertex. The equation for the axis of symmetry is x = h, where h is the x-coordinate of the vertex.
5. Identify the y-intercept by evaluating f(0). Since the function is f(x) = 3x^2 + 12x, substitute x = 0 to find the y-intercept. Also, find the x-intercepts by setting f(x) = 0 and solving for x.