1. The problem asks to find the values of $b$, $c$, and $d$ in the cubic function $y = x^3 + bx^2 + cx + d$ given its graph, and to find the coordinates where the curve crosses the y-axis. 2. The general form of a cubic function is $y = x^3 + bx^2 + cx + d$. The y-intercept occurs where $x=0$, so $y=d$ at that point. 3. To find $b$, $c$, and $d$, we use key points from the graph such as roots (where $y=0$) and the y-intercept. 4. Suppose the graph shows roots at $x=r_1$, $x=r_2$, and $x=r_3$. Then the cubic can be factored as $y = (x - r_1)(x - r_2)(x - r_3)$. 5. Expanding this product gives $y = x^3 - (r_1 + r_2 + r_3)x^2 + (r_1r_2 + r_2r_3 + r_3r_1)x - r_1r_2r_3$. 6. Comparing this with $y = x^3 + bx^2 + cx + d$, we identify: $$b = -(r_1 + r_2 + r_3), \quad c = r_1r_2 + r_2r_3 + r_3r_1, \quad d = -r_1r_2r_3$$ 7. The y-intercept is at $(0, d)$. Since the exact roots or points are not provided in the problem statement, the method above explains how to find $b$, $c$, and $d$ from the roots. Final answers depend on the specific roots from the graph. "slug": "cubic coefficients", "subject": "algebra", "desmos": {"latex": "y=x^3+bx^2+cx+d","features": {"intercepts": true,"extrema": true}}, "q_count": 3