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Standard form of Quadratic Function: y = ax 2 + bx + c

Ch 5 Pt 1 Portfolio Page – 5-1 through 5-5. Standard form of Quadratic Function: y = ax 2 + bx + c Quadratic term: ax 2 Linear term: bx Constant term: c Example: Determine if the function is linear or quadratic. State the quadratic, linear, and constant terms:

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Standard form of Quadratic Function: y = ax 2 + bx + c

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  1. Ch 5 Pt 1 Portfolio Page – 5-1 through 5-5 Standard form of Quadratic Function: y = ax2 + bx + c Quadratic term: ax2 Linear term: bx Constant term: c Example: Determine if the function is linear or quadratic. State the quadratic, linear, and constant terms: 1) f(x) = 3x2 – (x + 3)(2x – 1) Graph of a Quadratic Function: f(x) = x2 – 5x + 3; quadratic/ x2 / -5x / 3 (4, 1) X = 4 (2, 0) (8, -3) Parabola – the graph of a quadratic function (U-shaped) Axis of Symmetry -- the line that divides a parabola into two parts that are mirror images. Vertex – the point at which the parabola intersects the axis of symmetry. If graph opens up, vertex is MINIMUM. If graph opens down, vertex is MAXIMUM. Example: State vertex: State axis of symmetry: State P’ State Q’ P Q • Quadratic Regression on Graphing Calculator: Write a quadratic model given points on the graph. • In calculator: • 1) STAT / 1:Edit – enter x values in L1 and y values in L2 • 2) STAT / CALC / 5:QuadReg • 3) VARS / Y-VARS / 1:Function / 1:Y1 • 4) ENTER • Substitute values of a, b, and c into standard form. Y = -2x2 + 12 Graph: (y = ax2 + c) Ex: y = -x2 + 4 Graph from Standard Form: f(x) = ax2 + bx + c: If a is (+), parabola opens up. If a is (-), parabola opens down. Vertex: ( Axis of symmetry: x = Y-intercept: (0, c) Graph: (y = ax2 + bx + c) Ex: y = x2 + 2x - 6 V: (0, 4) Pts: (1, 3);(2, 0) V: (-1, -7)) Pts: (0, -6);(1, -3) M. Murray

  2. Vertex: (h, k) Axis of Symmetry: x = h Graph: y = -3(x+1)2 + 4 V: (-1, 4) Pts: (0, 1);(1, -8) Y = - V: (2, 3) Y-int: (0, 7) V: (1, 2) Y-int: (0, -1) Y = 2x2 + 6x + 4 Y = 2(x – 1)2 + 1 • To solve quadratic equations by factoring: • 1) Write equations in standard form (set = to zero) • 2) Factor • 3) Apply zero product property and set each variable factor to zero. • 4) Solve the equations 1) x2 = 16x – 48 2) 9x2 – 16 = 0 3) x2 – 5x + 2 = 0 x = 12, x = 4 x = • To solve by finding square roots: • 1) Isolate squared term on one side of equation • 2) Take the square root of each side. *don’t forget • To solve by Graphing: • 1) Graph the related function y = ax2 + bx + c • 2) Find ZEROS (x-intercepts): • 2nd/CALC/Zero • Left bound, Right bound, Guess M. Murray

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