# Graph of y=x^2

by Menos
Tags: graph
 Mentor P: 7,320 Start from the 2 point formula for a line. $$\frac {y - y_1} {x - x_1} = \frac {y_2 - y_1} {x_2 - x_1}$$ The formula for your parabola is $$y = x^2$$ So we can write $$y_1 = x_1^2$$ and $$y_2 = x_2^2$$ Use this information in the 2 point formula to get $$\frac {y - y_1} {x - x_1} = \frac {x_2^2 - x_1^2} {x_2 - x_1}$$ Note that the numerator on the Right Hand Side is the differenc of squares and can be factored to get $$\frac {y - y_1} {x - x_1} = \frac {(x_2 - x_1) (x_2 + x_1)} {x_2 - x_1}$$ Cancel like factors in the RHS $$\frac {y - y_1} {x - x_1} = (x_2 + x_1)$$ Now rearrange this to get $$y - y_1 = (x - x_1) (x_2 + x_1)$$ Simplify to get: $$y = x (x_2 + x_1) - x_1 x_2$$ Clearly you are correct for the simple parabola, in addition it can be seen that the slope of the line is the sum of the x coordinates.