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MATH Solutions By PHANI
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#🏆పోటీ పరీక్షల స్పెషల్
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![🏆పోటీ పరీక్షల స్పెషల్ - QUADRATIC FUNCTIONS BASIC NOIES MAIHL 1 3 What is a Quadratic Function? GraphofaQuadratic Function quadratic function is a function The graph of a quadratic function is parabola of degree 2 f(x)=aX bx+c, a#0 if @>O, parabola opens upward ifa <O, parabola opens downward Examples: F(x) = *+3*+2 Q>0 a<0 f(x)= 2x?- 5x+1 Standard Form a>0 a<० y=ax+bx+c where: Q,b,C are constants AxisofSymmetry QO line The passing through the vertex is Graphof aQuadratic Function called the axis of symmetry The graph of a quadratic function is a =0 K parabola 20 porobolo opens upward ifa>0, Zeroes] Roots if a<O, parabola opens downward The values of * for which Fo) =0 are called zeroes or roots So solve: + |62 ax 4aC X= 2a Q <೦ a>0 Vertex Discriminant The turning point of the porobolq is 4ac D= b3 The value b is called the discriminant Xvertex, 2a if D>O, two distinct real roots Step si # this volue into the function if D>o, equal real roots to get the yzcor if D<O, no real roots So roots are: <=1,3 Factor Form If roots are @ and B; then 10 Practice Question f(x)= @(x-@)(x-B) For f(x)=x-4x+3 Find the roots Example: *2-5*+6= (*-2)(*-3) *2-4*+3=0 (>-1)(>-3)=0 If you want, can make & So roots are: X=1,3 colourful poster for quadratic QUADRATIC FUNCTIONS BASIC NOIES MAIHL 1 3 What is a Quadratic Function? GraphofaQuadratic Function quadratic function is a function The graph of a quadratic function is parabola of degree 2 f(x)=aX bx+c, a#0 if @>O, parabola opens upward ifa <O, parabola opens downward Examples: F(x) = *+3*+2 Q>0 a<0 f(x)= 2x?- 5x+1 Standard Form a>0 a<० y=ax+bx+c where: Q,b,C are constants AxisofSymmetry QO line The passing through the vertex is Graphof aQuadratic Function called the axis of symmetry The graph of a quadratic function is a =0 K parabola 20 porobolo opens upward ifa>0, Zeroes] Roots if a<O, parabola opens downward The values of * for which Fo) =0 are called zeroes or roots So solve: + |62 ax 4aC X= 2a Q <೦ a>0 Vertex Discriminant The turning point of the porobolq is 4ac D= b3 The value b is called the discriminant Xvertex, 2a if D>O, two distinct real roots Step si # this volue into the function if D>o, equal real roots to get the yzcor if D<O, no real roots So roots are: <=1,3 Factor Form If roots are @ and B; then 10 Practice Question f(x)= @(x-@)(x-B) For f(x)=x-4x+3 Find the roots Example: *2-5*+6= (*-2)(*-3) *2-4*+3=0 (>-1)(>-3)=0 If you want, can make & So roots are: X=1,3 colourful poster for quadratic - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_537748_1d2883f2_1773710532676_sc.jpg?tenant=sc&referrer=pwa-sharechat-service&f=676_sc.jpg "🏆పోటీ పరీక్షల స్పెషల్ - QUADRATIC FUNCTIONS BASIC NOIES MAIHL 1 3 What is a Quadratic Function? GraphofaQuadratic Function quadratic function is a function The graph of a quadratic function is parabola of degree 2 f(x)=aX bx+c, a#0 if @>O, parabola opens upward ifa <O, parabola opens downward Examples: F(x) = *+3*+2 Q>0 a<0 f(x)= 2x?- 5x+1 Standard Form a>0 a<० y=ax+bx+c where: Q,b,C are constants AxisofSymmetry QO line The passing through the vertex is Graphof aQuadratic Function called the axis of symmetry The graph of a quadratic function is a =0 K parabola 20 porobolo opens upward ifa>0, Zeroes] Roots if a<O, parabola opens downward The values of * for which Fo) =0 are called zeroes or roots So solve: + |62 ax 4aC X= 2a Q <೦ a>0 Vertex Discriminant The turning point of the porobolq is 4ac D= b3 The value b is called the discriminant Xvertex, 2a if D>O, two distinct real roots Step si # this volue into the function if D>o, equal real roots to get the yzcor if D<O, no real roots So roots are: <=1,3 Factor Form If roots are @ and B; then 10 Practice Question f(x)= @(x-@)(x-B) For f(x)=x-4x+3 Find the roots Example: *2-5*+6= (*-2)(*-3) *2-4*+3=0 (>-1)(>-3)=0 If you want, can make & So roots are: X=1,3 colourful poster for quadratic QUADRATIC FUNCTIONS BASIC NOIES MAIHL 1 3 What is a Quadratic Function? GraphofaQuadratic Function quadratic function is a function The graph of a quadratic function is parabola of degree 2 f(x)=aX bx+c, a#0 if @>O, parabola opens upward ifa <O, parabola opens downward Examples: F(x) = *+3*+2 Q>0 a<0 f(x)= 2x?- 5x+1 Standard Form a>0 a<० y=ax+bx+c where: Q,b,C are constants AxisofSymmetry QO line The passing through the vertex is Graphof aQuadratic Function called the axis of symmetry The graph of a quadratic function is a =0 K parabola 20 porobolo opens upward ifa>0, Zeroes] Roots if a<O, parabola opens downward The values of * for which Fo) =0 are called zeroes or roots So solve: + |62 ax 4aC X= 2a Q <೦ a>0 Vertex Discriminant The turning point of the porobolq is 4ac D= b3 The value b is called the discriminant Xvertex, 2a if D>O, two distinct real roots Step si # this volue into the function if D>o, equal real roots to get the yzcor if D<O, no real roots So roots are: <=1,3 Factor Form If roots are @ and B; then 10 Practice Question f(x)= @(x-@)(x-B) For f(x)=x-4x+3 Find the roots Example: *2-5*+6= (*-2)(*-3) *2-4*+3=0 (>-1)(>-3)=0 If you want, can make & So roots are: X=1,3 colourful poster for quadratic - ShareChat")