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The set S consists of all multiples of 6. Which of the following sets are contained within S ?

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## The set S consists of all multiples of 6. Which of the following sets are contained within S ?

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**The set Sconsists 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 Reminder: Citizenship points start today. Please work quietly so others can focus.**Parabolas**y = ax2 + bx + c**Vertex**(axis of symmetry, max/min) y-intercept x-intercept x-intercept**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 alwaysc. y-int = ( 0,c)**To find the x-intercepts**• Set y equal to 0 and solve for x. • The most common methods for solving quadratic equations are by factoring or using the quadratic formula.**Width = w**Length = 5+w Area = 36 = l x w (5+w)(w) 5w + w2 = 36 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.**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? w2 + 5w - 36 = 0 (w + 9)(w - 4) = 0 W + 9 = 0 and w – 4 = 0 w=-9 and w=4 4 because dimensions cannot be negative.**Solving Using the Quadratic Formula**Example: 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 = -36**Max/Min**• If 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 Symmetryis the x-coordinate of the vertex. x = _____**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.**Properties of Parabolas**• x2 + 4x – 5 2) -x2 − 2x + 1