Find x-intercepts (roots) and y-intercept of linear, quadratic, and rational functions
Intercepts are where the graph crosses the coordinate axes. The y-intercept is always (0,f(0)). The x-intercepts are roots of f(x)=0. Together they provide key points for graphing functions.
The y-intercept is where the graph meets the y-axis (x=0). The x-intercepts are where it meets the x-axis (y=0). Intercepts are essential for sketching graphs and understanding function behavior near the axes.
Always (0, f(0)). For f(x)=ax+b: (0,b). For quadratics: (0,c). Exists if f defined at 0.
Solutions to f(x)=0. Linear: one. Quadratic: 0-2 real. Rational: numerator zeros excluding denominator zeros.
Intercepts are the easiest points to find when graphing. They anchor the graph on the coordinate axes.
Horizontal lines have no x-intercept (y=c, c!=0). Vertical lines have no y-intercept. Functions undefined at 0 have no y-intercept.
| Function Type | X-Intercept | Y-Intercept |
|---|---|---|
| Linear ax+b | x = -b/a | (0,b) |
| Quadratic ax^2+bx+c | Use roots or quadratic formula | (0,c) |
| Rational function | Set numerator = 0 and check denominator | Evaluate f(0), if defined |
| No real roots | No x-intercept | May still have a y-intercept |
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