Question

Draw the graph of the function f:R→R : f(x)=x²–6x+5. Obtain the coordinates of the points at which the graph meets the x and y axes.

Answer 1

x intersection:

$$y=0, x^2-6x+5=0$$ $$x_{1,2}=\frac {6 \pm \sqrt{6^2 - 4 \cdot 5}} {2} = \frac {6 \pm 4} {2}$$ $$x_1 =1, x_2 =5$$ $$(1,0) and (5,0)$$

y intersection:

$$x=0, y=0^2 - 5 \cdot 0 +5=5$$ $$(0,5)$$