Fill out the information below for the following quadratic function: f(x)=x2−4x−5 Complete the table below: xf(x)01234 Write the factored form of the function f(x)=?

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Fill out the information below for the following quadratic function:  f(x)=x2−4x−5  Complete the table below:  xf(x)01234  Write the factored form of the function  f(x)=?

Fasaniu · Accepted Answer

Step 1  Factoring quadratics is a method of expressing the polynomial as a product of its linear factors.  Factoring quadratics is a method of expressing the quadratic function  f(x)=ax2+bx+c  as a product of its linear factors as (x−k)(x−h), where h, k are the roots of the quadratic equation f(x)=0   Factorization of quadratic equations can be done using different methods such as splitting the middle term, using the quadratic formula, completing the squares, etc.  Step 2  Given: f(x)=x2−4x−5  Now, we have  for x=0  f(0)=−5  for x=1  f(1)=12−4(1)−5  =1−4−5  =−8K  for x=2  f(2)=22−4(2)−5  =4−8−5  =−9  for x=3  f(3)=32−4(3)−5  =9−12−5  =−8  for x=4  f(4)=42−4(4)−5  =16−16−5  =−5  Therefore,  xf(x)0−51−82−93−84−5  Step 3  Now,  f(x)=x2−4x−5  =x2−5x+x−5  =x(x−5)+1(x−5)  =(x−5)(x+1)  Answer: ∴f(x)=(x−5)(x+1)

Mollie Nash · Accepted Answer

Step 1f(x)=x2−4x−5Find the properties of the given parabola.Rewrite the equation in vertex form.Complete the square for&amp;nbsp;x2−4x−5Use the form&amp;nbsp;ax2=bx+c, to find the values of a, b, and ca=1,&amp;nbsp;b=−4,&amp;nbsp;c=−5Consider the vertex form of a parabola.a(x+d)2+eSubstitute the values of a and b into the formulad=b2ad=−42(1)Simplify the right side.Cancel the common factor of 4 and 2Factor 2 out of 4d=−2×22×1Cancel the common factors.Factor 2 out of&amp;nbsp;2×1d=−2×22(1)Cancel the common factor.d=−2×22×1Rewrite the expression.d=−21Divide 2 by 1d=−1×2Multiply -1 by 2d=−2Step 2Find the value of e using the formulae=c−b24aSimplify each term.Cancel the common factor of&amp;nbsp;(−4)2&amp;nbsp;and 4Rewrite -4 as&amp;nbsp;−1(4)e=−5−(−1×4)24(1)Apply the product rule to&amp;nbsp;−1(4)e=−5−(−1)2×424(1)Raise -1 to the power of 2e=−5−1×424(1)Multiply&amp;nbsp;42&amp;nbsp;by 1e=−5−424(1)Factor 4 out of&amp;nbsp;42e=−5−4×44(1)Cancel the common factors.e=−5−4×44×1Rewrite the expression.e=−5−41Divide 4 by 1e=−5−1×4Multiply -1 by 4e=−5−4Subtract 4 from -5e=−9Substitute the values of a, d, and e into the vertex form&amp;nbsp;a(x+d)2+e(x−2)2−9Set y equal to the new right sidey=(x−2)2−9Use the vertex form&amp;nbsp;y=a(x−h)2+k, to determine the values of a, h, and ka=1&amp;nbsp;

Fill out the information below for the following quadratic function: f(x)=x^{2}-4x-5 Complete

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