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Completing the square

completing the square examples

Subject: 
Algebra
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Mathematics
Elementary algebra
Completing the square
Equation solving
Square root

Ex 2: f(x)= 7x2 +28x+56 o X1-F4(tsl' - - ? 510 71-J 2 +q)c -- (9'' H 84- x L +Lfx+ i F-4 = F( T *?g J?Z t r?q - = )C+z H Fx ?2? j Section 4-5: Solving with Completing the Square The Process 1) Set equation 0 2) Shove the constants to the other side 3) Get the Leading Coefficient to be 1 4) Complete the Square. Then add that value to both sides. 5) Take the square root of both sides and solve for x. For Examples 1-5 Find the solutions to the quadratic. Ex 1: f(x) = 3x2 + 42x + 24 0 3tL) 4- 2 ( - _ +r~ X Ex 3: g(x)=6x2 +6x+12 0 ('x 2. +LocW - xt / \ 1.- 2. - :+? - 9 '4 ( / X OL 0 Section 4-5: Solving with Completing the Square Ex4:y=x2 +7x+2 Ex5:f(x)=3x2 -12x+l O3x/yl

completing the square

Subject: 
Algebra
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Mathematics
Elementary algebra
Algebra
Completing the square
Quadratic function
Factorization
Polynomial expansion
Partial fraction decomposition

Section 4.5: Vertex form with Completing the Square Completing the Square: Used to change quadratic functions in standard form to vertex form. f (x) = ax 2 + bx + c - f(x)=a(x?h) 2 +k ------------------------ Investigation This creates a Perfect Square 2 (b)2 Tririomiai, which factors To complete the square for an expression x + bx, add ------ Startwithx2 + bx Find (b)2 x2 +bx+() (x+ )2 / The Completed Square Factored form x2 +6x - x2 +4x 2 X - 8x _) - X - 2x oF W4CX 1rrrt! You Try?Complete the Square for the following. Then write the factored form. 1)x2 +14x 2)y2 +20y 2t\2S io) IOD (xiiJJ _ 0) 3)m2 -IOM L Omtn - 15 ) ;4 6 7 4)h2 -15h '4 P7 L_'1-' & ? **How do we go from standard form of mAquation to vertex form?

graph quadratics in vertex form

Subject: 
Algebra
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Mathematics
Graph theory
Elementary algebra
Elementary mathematics
Parabolas
Quadratic function
Analytic geometry
Y-intercept
Completing the square
Cartesian coordinate system
Geometry of roots of real polynomials

3 H 5 Vt4Section 4.7: Graph of Quadratic Functions in Vertex or Intercept rm. J *Reca ll the transformations from Section 2.7 we learned f(x) = a I x - hi + Ic for absolute value functions. Vertex Form of a Quadratic f(x) =' (x - h)2 + ? Vertex: -Kit itc'1eS-- 0 r 2f4oO&1 Axis of Symmetry: In 0 *l.L tot,&) J'&H- ? Opens up/down if: Example 1: Given f(x) = x2, write it in vertex form and graph. totAJe-k- polv1+ on hne con1-aiw\k -' 4?LiOOlO?' j x ' - t 03 I \ z_ (oo) h t. Example 2: Given f(x) = (x - 3)2 - 5, state the vertex and axis of symmetry, describe the translations, and graph. (h,-) Vertex: (y) Axis of Symm: 3 Translations: 110flZ0iT1t'A 1 (C\\* 3 \rc&k C1$SIO(\ Vi (extjj \- CoLJJfl .iej~ 5o~ I ~~ k q I
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