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

The form of f(x) is f(x) = 2(x - 5)² + 4Step-by-step explanation:The vertex form of a quadratic function f(x) = ax² + bx + c isf(x) = a(x - h)² + k, wherea is the coefficient of x²(h , k) are the coordinates of its vertex point[tex]h=\frac{-b}{2a}[/tex] , where b is the coefficient of xk = 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∵ [tex]h=\frac{-b}{2a}[/tex]∴ [tex]h=\frac{-(-20)}{2(2)}[/tex]∴ [tex]h=\frac{20}{4}[/tex]∴ h = 5To 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 = 4Substitute 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 + 4The form of f(x) is f(x) = 2(x - 5)² + 4Learn more:You can learn more about quadratic function in brainly.com/question/9390381#LearnwithBrainly