Solving equations

Proportion

An equation with two ratios, fractions, set equal to each other. 1/5=2/10 is a proportion.

What is an issue with squaring each side of an equation.

Because squaring a value can turn a negative value into a positive value squaring both sides can make an untrue equation into a true equation, making the solution wrong. Such as if you were to square the equation 5=-5. Squaring this statement would make the equation true---which it is not so you have to be careful when squaring equations.

If niether c or b are equal to 0 in a quadratic equation, what method is most commonly used to solve it.

Factoring

When the c in a quadratic equation is equal to 0 what method is most commonly used to solve the quadratic.

Factoring

Reciprocal

If two numbers are reciprocals to each other that means when multiplied together the product is 1. The value 5 and 1/5 are reciprocals because the product of the two is 1.

Solve for y if 9y^2 - 12y + 4 = 0 is true

Multiply 9 and 4 to get 36 and figure out what multiplies to get 36 and adds up to -12 whch is -6 and -6. Re-arrange the equation to get 9y^2 -6y + -6y +4 re-arrange again to get 3y(3y-2) + -2(3y - 2) re-arrange into binomials to get (3y-2)(3y-2) USe the MPZ to get the double-root solution 2/3

When the b in a quadratic equation is equal to 0 what method is most commonly used to solve the quadratic.

Normally, you square both sides of the equation to get rid of the second-degree and then solve normally from there.

Double root

One solution that is counted twice in a quadratic equation because it had two different solutions but they were the same value.

Multiplecation property of 0/MPZ

Property that states if qz=0 then either q, z or both values are equal to 0.

What is a special feature about quadratics involving their solution.

Quadratics can have more than one solution to an equation.

Principle square root of a number

The positive value that when multiplied by itself gives you the value that was being squared.

What do perfectly squared binomials tell you about the solution to the equation

The solution will be double-root

What do the graphs of quadratics look like

They are u shaped (called a parabola) with an extreme point thats highest, lowest, farthest left or farthest right.

Use the MPZ property to solve for x if x(x-5)=0 is true

This states that either x-5 must be equal to 0 or x must be equal to 0. If x-5=0 then x must be equal to 5, so 5 is one solution. The other solution would be if x were equal to zero. So the two solutions are 0 and 5.

Quadratic formula

X=-b + or - Square root of b^2-4ac/2a

What is soemthing you have to do to a value when you take the square root of it.

You have to put a negative and positive sign in front of it because both a negative and a positive value could be the result and you wouldnt be able to know.

What if a trinomial quadratic cant be factored

You use the quadratic formula

How would you solve the quadratic x^2-3x=28

You would have to factor because niether b or c is equal to 0. The best method is to get one side of the equation equal to 0 so first subtract 28 to get x^2-3x-28=0. Then you factor by un-distributing the equation back into a binomial. Because the coefficient for the first term is 1, you can assume that the first value in the binomial is x and x like so (x, )(x, ) Then you figure out what multiplies to get - 28 and adds up to -3 which is -7 and 4, then re-arrange the equation to get x^2 -7x + 4x -28. Seperate the first two and last two terms by factoring out the GCF to get x(x-7) + 4(x-7) Factor agian to get the binomial (x+4)(x-7) Then solve for x using the multiplecation property of 0. If x+4 = 0 then the solution is -4 If x-7 = 0 then the solution is 7 So, the solutions are -4 and 7

What is the standard form of a linear equation

ax+b=c a cannot be equal to zero because then it would not be a linear equation.