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Core Connections Algebra 2, 2013

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Core Connections Algebra 2, 2013 View details

1. Section 2.1

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Exercise 35 Page 69

Practice makes perfect

a When we have a quadratic equation written in the form x^2+bx=0, we can solve this by factoring out the variable and then solving the resulting equation with the Zero Product Property.

y^2-6y=0

Factor out y

y(y-6)=0

Use the Zero Product Property

lcy=0 & (I) y-6=0 & (II)

(II): LHS+6=RHS+6

ly_1=0 y_2=6

b Notice that both sides of the equation contain a 7. Therefore, if we subtract 7 from both sides, we end up with an equivalent equation but without a constant. This can be solved by the Zero Product Property like we did in Part A.

n^2+5n+7=7

LHS-7=RHS-7

n^2+5n=0

Factor out n

n(n+5)=0

Use the Zero Product Property

lcn=0 & (I) n+5=0 & (II)

(II): LHS-5=RHS-5

ln_1=0 n_2=-5

c Like in Part B, we can solve this with the Zero Product Property if we first eliminate the constant from both sides.

2t^2-14t+3=3

LHS-3=RHS-3

2t^2-14t=0

Factor out 2t

2t(t-7)=0

.LHS /2.=.RHS /2.

t(t-7)=0

Use the Zero Product Property

lct=0 & (I) t-7=0 & (II)

(II): LHS+7=RHS+7

lt_1=0 t_2=7

d Like in Parts B and C, we can solve this equation with the Zero Product Property if we first eliminate the constant from both sides.

1/3x^2+3x-4=-4

LHS+4=RHS+4

1/3x^2+3x=0

LHS * 3=RHS* 3

x^2+9x=0

Factor out x

x(x+9)=0

Use the Zero Product Property

lcx=0 & (I) x+9=0 & (II)

(II): LHS-9=RHS-9

lx_1=0 x_2=-9

e Graphically, the solutions to a quadratic expression set equal to zero are its x-intercepts. Since all of the quadratic equations are without a constant, this means they intercept the y-axis at the origin, which also constitutes one of the x-intercepts.

Subchapter links

2.1.1 Modeling Non-Linear Data p.58-59

2.1.2 Parabola Investigation p.63-65

2.1.3 Graphing a Parabola Without a Table p.69-70

2.1.4 Rewriting in Graphing Form p.76-78

2.1.5 Mathematical Modeling with Parabolas p.81-82