<span>The equation for a parabola is y = ax^2+ bx + c
In this example, y = x^2 - 4x + 3
a = 1
b = -4
c = 3
Because "a" is a positive number, the parabola will open upwards and the vertex will be a minimum (at the bottom).
To find the vertex, use x = -b/2a
x = -(-4) / 2 (1)
x = 4 / 2
x = 2
Then solve for y using x = 2
y = x^2 - 4x + 3
y = 2^2 - 4(2) + 3
y = 4 - 8 + 3
y = -1
Therefore the vertex (x,y) is at (2, -1)
To find the x intercept, let y = 0 and solve for x.
y = x^2 - 4x + 3
0 = x^2 - 4x + 3
0 - (x^2 - 4x + 3) = x^2 - 4x + 3 - (x^2 - 4x + 3)
-x^2 + 4x - 3 = 0
Factor left side of equation:
(-x + 1)(x - 3) = 0
Therefore
-x + 1 = 0 or x - 3 = 0
x = 1 or x = 3
The x intercepts are (1,0) and (3,0).</span>
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