Respuesta :

chetankachana

Answer:

f(x) = 1(x - 4.5)² - 6.25

Step-by-step explanation:

Hello!

Let's find the Vertex Form of the quadratic by Completing the Square.

  • f(x) = x² - 9x + 14
  • x² - 9x + 14 = 0
  • x² - 9x = -14

The formula for a Perfect Square Trinomial is (a+b)² = a² + 2ab + b².

To find b², we need to divide -9 by 2 and square it.

  • -9
  • -4.5
  • 20.25

Add this number to both sides and factor. Remember, the b term here is simply half of the b term in the equation (-4.5).

  • x² - 9x + 20.25 = -14 + 20.25
  • (x - 4.5)² = 6.25
  • (x - 4.5)²- 6.25 = 0

Convert this back to function form:

  • f(x) = 1(x - 4.5)² - 6.25

The equation is f(x) = 1(x - 4.5)² - 6.25.

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