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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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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

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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