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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Analyzing Functions with Successive Differences

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Exercise 40 Page 145

Make sure you write all the terms on the left-hand side of the equation and simplify as much as possible before using the Quadratic Formula.

-2 and 2.5

Practice makes perfect

We will use the Quadratic Formula to solve the given quadratic equation. ax^2+ bx+ c=0 ⇕ x=- b± sqrt(b^2-4 a c)/2 aWe first need to identify the values of a, b, and c. 6x^2-3x-30=0 ⇕ 6x^2+( - 3)x+( - 30)=0 We see that a= 6, b= - 3, and c= - 30. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( -3)±sqrt(( - 3)^2-4( 6)( - 30))/2( 6)

▼

Solve for x and Simplify

- (- a)=a

x=3±sqrt((- 3)^2-4(6)(- 30))/2(6)

Calculate power

x=3±sqrt(9-4(6)(- 30))/2(6)

Multiply

x=3±sqrt(9-24(- 30))/12

MultNegNegOnePar

- a(- b)=a* b

x=3±sqrt(9+720)/12

Add terms

x=3±sqrt(729)/12

Calculate root

x=3± 27/12

Factor out 3

x=3(1± 9)/12

CancelCommonFac

Cancel out common factors

x=1± 9/4

Using the Quadratic Formula, we found that the solutions of the given equation are x= 1± 94. Therefore, the solutions are x_1= 104=2.5 and x_2= -84=-2.

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Exercises p.143-145