Question

quiz 4-1: graphing, factoring, & square roots methods
for questions 1-2, find the roots by graphing.

1. $f(x)=x^2-8x+12$
2. $f(x)=-2x^2-4x-2$

for questions 3-12, solve by factoring

1. $x^2+5x-36=0$
2. $x^2+61=1-17x$
3. $3x^2+112=2x^2+22x$
4. $2x^2+7x=42-x$
5. $12x^2+17x=5$
6. $25x^2=20x-4$

Explanation:

Questions 1-2 (Roots by Graphing)

Step1: Factor quadratic for roots

For $f(x)=x^2-8x+12$:
$x^2-8x+12=(x-2)(x-6)$
Set to 0: $(x-2)(x-6)=0$

Step2: Identify roots from factors

Roots are $x=2$ and $x=6$ (graph crosses x-axis at these points)

Step1: Simplify quadratic for roots

For $f(x)=-2x^2-4x-2$:
First factor out -2: $-2(x^2+2x+1)=-2(x+1)^2$
Set to 0: $-2(x+1)^2=0$

Step2: Identify repeated root

Root is $x=-1$ (graph touches x-axis at this point)

Question3: Factor trinomial

$x^2+5x-36=0$
Find factors of -36 that sum to 5: 9 and -4
$(x+9)(x-4)=0$
Set each factor to 0: $x+9=0$ or $x-4=0$

Question4: Rearrange to standard form

$x^2+17x+60=0$
Find factors of 60 that sum to17: 12 and5
$(x+12)(x+5)=0$
Set each factor to 0: $x+12=0$ or $x+5=0$

Question5: Rearrange to standard form

$x^2-22x+112=0$
Find factors of 112 that sum to -22: -14 and -8
$(x-14)(x-8)=0$
Set each factor to 0: $x-14=0$ or $x-8=0$

Question6: Rearrange to standard form

$2x^2+8x-42=0$
Divide by 2: $x^2+4x-21=0$
Find factors of -21 that sum to4:7 and -3
$(x+7)(x-3)=0$
Set each factor to 0: $x+7=0$ or $x-3=0$

Question7: Rearrange to standard form

$12x^2+17x-5=0$
Use AC method: $12x^2+20x-3x-5=0$
Factor by grouping: $4x(3x+5)-1(3x+5)=0$
$(4x-1)(3x+5)=0$
Set each factor to 0: $4x-1=0$ or $3x+5=0$

Question8: Rearrange to standard form

$25x^2-20x+4=0$
Perfect square trinomial: $(5x-2)^2=0$
Set factor to 0: $5x-2=0$

Answer:

1. $x=2$ and $x=6$
2. $x=-1$

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Questions 3-8 (Solve by Factoring)