Write f(x) = x² - 3x + 2 into vertex form?

Solution:

The vertex form of a quadratic function is f(x) = a(x - h)² + k where a, h, and k are constants. The vertex of the parabola is at (h, k). 

When the quadratic parent function f(x) = x²  is written in the vertex form , y = a(x - h)²  + k, a = 1, h = 0 and k = 0.

For the given quadratic equation  f(x) = x² - 3x + 2 the x coordinate of the vertex is given by the expression:

x = -b/2a

Where b = -3 and a = 1

x = h = -(-3)/2(1) = 3/2

Substituting the value of x in the given quadratic equation we get the value of the y coordinate which is

k = y = f(x) = (3/2)² - 3(3/2) + 2 = 9/4 - 9/2 + 2

k = -9/4 + 2 = -1/4 

The vertex is therefore (3/2, -1/4)

Now we have all the constants required to write the vertex form of the equation:

a = 1, h = 3/2 and k = -¼

The vertex form of the quadratic equation is:

(1)(x - 3/2)² - 1/4 
= (x - 3/2)² - 1/4

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Write f(x) = x² - 3x + 2 into vertex form?

Summary:

The vertex form of the quadratic equation is (x - 3/2)² - 1/4