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Graph y = x² − 4x + 3

Find the intercepts, vertex, and axis of symmetry before graphing a quadratic.

Graph y = x² − 4x + 3

Method: Factoring and vertex form

Step-by-step solution

1
Find the x-intercepts
Factor the quadratic as (x−1)(x−3), so the roots are 1 and 3.
2
Find the vertex
Complete the square to write y=(x−2)²−1.
$y=(x-2)^2-1$
3
Use symmetry
The axis is x=2 and the positive leading coefficient makes the parabola open upward.

ext{vertex }(2,-1),quad x ext{-intercepts }1,3

The intercepts and vertex determine the main shape and provide exact checkpoints for the plot.

Reading x−2 as a shift left reverses the horizontal transformation.

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