Question

which feature on a graph is used to determine the roots of an equation?

y-intercept
vertex
x-intercept
slope

Explanation:

To determine the roots of an equation from its graph, we look for the points where the graph intersects the \(x\)-axis. These intersection points are called the \(x\)-intercepts, and the \(x\)-values at these points are the roots of the equation. The \(y\)-intercept is where the graph crosses the \(y\)-axis (when \(x = 0\)), the vertex is a characteristic of parabolas (for quadratic functions) and not directly related to finding all roots, and the slope is related to the rate of change of a linear function, not root - finding.

Answer:

\(x\)-intercept