S consists of all multiples of 6 Which of the following sets are contained within S The set of all multiples of 3 The set of all multiples of 9 The set of all multiples of 12 ID: 246935
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Slide1
The set S consists of all multiples of 6. Which of the following sets are contained within S ?
The set of all multiples of 3The set of all multiples of 9The set of all multiples of 12
Reminder:
Citizenship points start today.
Please work quietly so others can focus.Slide2Slide3Slide4Slide5Slide6Slide7
Parabolas y = ax
2 + bx + cSlide8
Vertex
(axis of symmetry, max/min)
x
-intercept
x
-intercept
y-interceptSlide9
Properties of a ParabolaSlide10
To Find the y-intercept:1) Write the equation in standard form, set x equal to 0 and solve for y.
2) The y-intercept is always c.y-int = ( 0, c
)Slide11
To find the x-interceptsSet y equal to 0 and solve for x.The most common methods for solving quadratic equations are by factoring or using the quadratic formula. Slide12
The length of a rectangular window is 5 feet more than its width, w. The area of the window is 36 square feet. Write an equation that can be used to find the dimensions of the window.
Width = wLength = 5+wArea = 36 = l x w (5+w)(w)5w + w2 = 36Slide13
Solve for w: 5w + w2 = 36 Rearrange equation to set it equal to zero.
Factor to get: In order for the product to equal 0, at least one of the factors has to be 0.So you have Therefore, Which answer makes more sense and why?
(w + 9)(w - 4) = 0
w
2
+ 5w - 36 = 0
w=-9 and w=4
4 because dimensions cannot be
negative.
W + 9 = 0 and w – 4 = 0Slide14
Solving Using the Quadratic FormulaExample: 5w + w2 =
36 → w2 + 5w - 36 = 0 For ax2 + bx + c = 0, the value of x is given by:
Step 1: Note that
Step 2: Substitute
a = 1, b = 5,
&
c = -36Slide15
Step 3: SimplifyStep 4: Solve
Slide16
Max/MinIf a is positive, the graph opens upward (smile) and you will have a min.If a is negative, the graph opens downward
(frown) and you will have a max.The max/min is the y-coordinate of the vertex. y = ____The Axis of Symmetry is the x-coordinate of the vertex. x = _____Slide17
To find the Vertex… 1) Use to find the x- coordinate. 2) Plug the x-coordinate into the original equation and solve to find the y-coordinate.Slide18
Properties of Parabolasx2 + 4x – 52) -x2 − 2x + 1