Sketch the graph of the function y = x^{2} − 6x + 4

Step 1 Does not factorise so... complete the square by adding 5 to both sides.

y + 5 = x^{2} − 6x + 4 + 5 y + 5 = x^{2} − 6x + 9 y + 5 = (x − 3)² y = (x − 3)² − 5 So the graph is the basic parabola y = x ² moved forward 3 anddown 5

Step 2 Find the intercepts Put x = 0 into the equation.

y = (x − 3)² − 5 y = (0 − 3)² − 5 y = 9 − 5 y = 4 The y-intercept is 4

Step 3 Put y = 0 into the equation.

0 = (x − 3)² − 5 5 =(x − 3)² ±√ 5 = x − 3 x = 3 ±√ 5 x = 5.24 or 0.76 (to 2 d.p.) The x-intercepts are 5.24 and 0.76