Question

Express f(x) in the form a(x-h)^2+k for f(x)= 2x^2-20x+54

Answer 1

The form of f(x) is f(x) = 2(x - 5)² + 4

Step-by-step explanation:

The vertex form of a quadratic function f(x) = ax² + bx + c is

f(x) = a(x - h)² + k, where

• a is the coefficient of x²
• (h , k) are the coordinates of its vertex point
• $h=\frac{-b}{2a}$ , where b is the coefficient of x
• k = f(h), that means the value of f(x) when x = h

∵ f(x) = 2x² - 20x + 54

∴ a = 2 , b = -20 and c = 54

- Find h and k

∵ $h=\frac{-b}{2a}$

∴ $h=\frac{-(-20)}{2(2)}$

∴ $h=\frac{20}{4}$

∴ h = 5

To find substitute x by 5 in f(x)

∵ f(5) = 2(5)² - 20(5) + 54

∴ f(5) = 2(25) - 100 + 54

∴ f(5) = 50 - 100 + 54 = 4

∵ k = f(h)

∴ k = 4

Substitute a, h, and k in the form f(x) = a(x - h)² + k

∵ a = 2 , h = 5 , k = 4

∴ f(x) = 2(x - 5)² + 4

The form of f(x) is f(x) = 2(x - 5)² + 4

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You can learn more about quadratic function in brainly.com/question/9390381

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