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FUNCTIONS AND THEIR GRAPHS NOTES Pythagorean Theorem- For a right triangle with hypotenuse c and length sides a and b. Formula: a^2+b^2=c^2 Distance Formula- To find the distance d between the points (x1,y1) and (x2,y2) in the plane. Formula: d=√(x2 −x1)^2 +(y2 −y1)^2 Midpoint Formula- To find the midpoint of the line segment joining the points (x1,y1) and (x2,y2). Formula: GRAPH OF AN EQUATION Graph of an equation- The set of all points that are solutions of the equation. To determine the solution points, you need to: o Write the original equation o Substitute the points for x and y o Simplify o If they are equal, it’s a solution. o If they are not equal, it’s not a solution. Point-plotting method- The basic technique used for sketching the graph of an equation. The point-plotting method of graphing: o When possible, isolate one of the variables o Construct a table of values showing several solution points o Plot these points in a rectangular coordinate system o Connect the points with a smooth curve or line Intercepts- Solution points of an equation that have zero as either the x-coordinate or the y-coordinate. Is possible for a graph to have no intercepts, one intercept, or several intercepts. Finding Intercepts- To find x-intercepts: o Let y be zero and solve the equation for x