Question

Rewrite the function by completing the square. f (x)= x^2 - 9x + 14

f (x) = _ ( x + _ )^2 + _

Answer 1

f(x) = 1(x - 4.5)² - 6.25

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.