College Algebra Chapter 1

Quadratic equation

ax^2+bx+c=0 a not equal to 0

Zero Product Property

A*B=0 and A=0 or B=0

solve ax^2+bx+c completing the square

subtract c from both sides, divide both sides by the leading coeficiant a, Compare (1/2, b/a)^2 add the result to both sides, factor left hand side as a binomial square; simplify right-hand side , solve using the square root property of equality

Quadratic formula

x=-b+- b^2-4ac/2a

Discriminant of the Quadratic formula

for ax^2+bx+c=0 anot equal to 0, If b^2-4ac=0, the equation has one real root.If b^2-4ac is greater than 0 the equation has two real rootsIf b^2-4ac is less than 0 the equation has two complex roots.

Summary of solution methods for ax^2+bx+c=0

If b=0, isolate x and use the square root property of equality.If c=0, factor out the GCF and solve using the zero product property.If no coefficient is zero, you can attempt to solve, factoring the trinomial, completeing the square, using the quadratic formula

Solving rational equations

1. Identify and exclude any values that cause a zero denominator. 2. Multiply both sides by LCD and simplify (this will eliminate all denominators. 3. Solve the resulting equation. 4. check all solutions in the original equation.

Extraneous roots

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Power property of Equality

If nsquare root and v are real-valued exspressions and n square root u =v then (n square root u)^n = v^n U=v^nfor n is greater than or equal to 2

pg 20

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Midpoint formula

m:(xsub1+xsub2/2, ysub1+ysub2/2)

distance formula

d=square root (xsub2-xsub1)^2+(ysub2-ysub1)^2

Equation of a circle

A circle of the radius r with the center at (h,k) has the equation (x-h)^2+(y-k)^2=r^2

diamter

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solving application of Variation

write the information given as an equation, using k as the constant multiple. Substitute the first relationship (pair of values) given and solve for k. Substitute this value for k in the original equation to obtain the variation equation. Use the variation equation to complete the application.

y varies inversly with x, or y is inversly proportional to x, If there is a nonzero constant k such that y=k(1/x) k is called the constant of variation.

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r=1/2 the diameter

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midpoint of diameter=center of circle

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y varies directly with x or y is directly proportional to x, if there is a nonzero constant k such that

y=kx