Answer:
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.
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.