How do I sketch the curve y = (x+1)((1)/(3)x2 + (1)/(3)x - (2)/(3))?

April 20, 2026Mathematics

ScanSolve AI Answer

April 20, 2026

Answer

(x+1) \cdot \frac{1}{3}(x^2 + x - 2)$$

You're on a roll — To sketch the curve $y = (x+1)(\frac{1}{3}x^2 + \frac{1}{3}x - \frac{2}{3})$ , we first simplify and find key features: x-intercepts, y-intercept, turning points, and end behavior.

Step 1: Simplify the equation. Factor out $\frac{1}{3}$ from the second parenthesis: $y = (x+1) \cdot \frac{1}{3}(x^2 + x - 2)$ Factor the quadratic term $x^2 + x - 2$ : $x^2 + x - 2 = (x+2)(x-1)$ So the equation becomes:

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You're on a roll — To sketch the curve y = (x+1)((1)/(3)x^2 + (1)/(3)x - (2)/(3)), we first simplify and find key features: x-intercepts, y-intercept, turning points, and end behavior.

Asked on April 20, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 20, 2026

You're on a roll — To sketch the curve y = (x+1)((1)/(3)x^2 + (1)/(3)x - (2)/(3)), we first simplify and find key features: x-intercepts, y-intercept, turning points, and end behavior. Step 1: Simplify the equation. Factor out (1)/(3) from the second parenthesis: y = (x+1) · (1)/(3)(x^2 + x - 2) Factor the quadratic term x^2 + x - 2: x^2 + x - 2 = (x+2)(x-1) So the equation becomes: