Find the Standard Form of the Parabola f(x)=x^2-8x

Problem

ƒ(x)=x2−8*x

Solution

1. Identify the coefficients of the quadratic function ƒ(x)=a*x2+b*x+c where a=1 and b=−8

2. Calculate the value needed to complete the square by taking half of the linear coefficient b and squaring it.

b/2=(−8)/2=−4

(−4)2=16

3. Add and subtract this value within the expression to maintain equality.

ƒ(x)=(x2−8*x+16)−16

4. Factor the perfect square trinomial into the form (x−h)2

x2−8*x+16=(x−4)2

5. Rewrite the function in the standard (vertex) form ƒ(x)=a*(x−h)2+k

ƒ(x)=(x−4)2−16

Final Answer

ƒ(x)=(x−4)2−16

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