QuestionsQuestion 1Find the maximum or minimum value of the following quadratic functions by completing square:(i)f(x)=x2+6x+13f(x)=x^2+6x+13f(x)=x2+6x+13(ii)f(x)=x2+4xf(x)=x^2+4xf(x)=x2+4x(iii)f(x)=−x2+8x+13f(x)=-x^2+8x+13f(x)=−x2+8x+13(iv)f(x)=−x2−3x−5f(x)=-x^2-3x-5f(x)=−x2−3x−5(v)f(x)=3x2+6x−13f(x)=3x^2+6x-13f(x)=3x2+6x−13(vi)f(x)=−2x2−x+21f(x)=-2x^2-x+21f(x)=−2x2−x+21SolutionTheoryQuestion 2Find the maximum or minimum point by sketching the following quadratic functions. Also find their domain and range:(i)f(x)=x2−4xf(x)=x^2-4xf(x)=x2−4x(ii)f(x)=x2−5x+6f(x)=x^2-5x+6f(x)=x2−5x+6(iii)f(x)=−x2+2x−8f(x)=-x^2+2x-8f(x)=−x2+2x−8(iv)f(x)=x2−4x+4f(x)=x^2-4x+4f(x)=x2−4x+4(v)f(x)=x2+2x−8.3f(x)=x^2+2x-8.3f(x)=x2+2x−8.3(vi)f(x)=6−x−x2f(x)=6-x-x^2f(x)=6−x−x2SolutionTheoryQuestion 3Find the inverse of the following quadratic functions. Also find their domain and range:(i)f(x)=x2−3, x≤0f(x)=x^2-3,\; x\le 0f(x)=x2−3,x≤0(ii)f(x)=x2+6x+4, x<−3f(x)=x^2+6x+4,\; x<-3f(x)=x2+6x+4,x<−3(iii)f(x)=2x2−8x+11, x≥2f(x)=2x^2-8x+11,\; x\ge 2f(x)=2x2−8x+11,x≥2(iv)f(x)=3x2−2x+6, x≥5f(x)=3x^2-2x+6,\; x\ge 5f(x)=3x2−2x+6,x≥5(v)f(x)=2(x−3)2+1, x≥3f(x)=2(x-3)^2+1,\; x\ge 3f(x)=2(x−3)2+1,x≥3(vi)f(x)=−3(x+4)2−5, x<−4f(x)=-3(x+4)^2-5,\; x<-4f(x)=−3(x+4)2−5,x<−4SolutionTheoryQuestion 4Solve the following absolute value quadratic equations and inequalities:(i)∣x2+1∣=5|x^2+1|=5∣x2+1∣=5(ii)∣x2+5x+4∣=0|x^2+5x+4|=0∣x2+5x+4∣=0(iii)∣x2−6x+8∣=4|x^2-6x+8|=4∣x2−6x+8∣=4(iv)∣3x2−7x+2∣=x2−x+1|3x^2-7x+2|=x^2-x+1∣3x2−7x+2∣=x2−x+1(v)∣x2−4∣<5|x^2-4|<5∣x2−4∣<5(vi)∣x2−3x+2∣>4|x^2-3x+2|>4∣x2−3x+2∣>4(vii)∣x2−5x+6∣≤x+2|x^2-5x+6|\le x+2∣x2−5x+6∣≤x+2(viii)∣2x2−3x−5∣<4|2x^2-3x-5|<4∣2x2−3x−5∣<4SolutionTheory