To find the roots of the equation 3x^2 = -24x - 34 using the features of the graph, we can first rearrange the equation in standard form as follows:
3x^2 + 24x + 34 = 0
We can then plot the corresponding quadratic function on a graph, which will be a downward-facing parabola, since the coefficient of the x^2 term is positive (3).
Next, we can use the features of the graph to estimate the roots of the equation. The roots of a quadratic equation are the x-values where the corresponding function crosses the x-axis. In other words, the roots are the solutions to the equation where y = 0.
To find the roots of the equation using the graph, we can look for the x-intercepts of the corresponding function. The x-intercepts are the points where the function crosses the x-axis, or where y = 0.
We can see from the graph that the quadratic function intersects the x-axis at two points, which are the roots of the equation. We can estimate the x-coordinates of these points by looking at where the function crosses the x-axis. We can also use the symmetry of the parabola to find the distance between the roots.
Once we have estimated the x-coordinates of the roots, we can use algebraic methods, such as factoring or the quadratic formula, to find their exact values.