Sketch the graph of the function y = x^{2} − 6x + 8

Step 2 Find the interceptsPut x = 0 into the equation.

y = 0^{2} − 6 x 0 + 8y = 8The y-intercept is 8

0 = (x − 4)(x − 2)x = 4 or x = 2The x-intercepts are 4 and 2

Step 3 Axis of symmetry is always midway between the x-intercepts.

Average of x-intercepts= (2 + 4)÷ 2 = 3

Axis of symmetry is the line x = 3

Step 4 Find the coordinates of the vertex.

The vertex occurs at x = 3When x = 3y = (3 − 4)(3 − 2)y = -1The vertex is at the point (3, -1)

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