By: Adam Linnabery

The quadratic formula is –b+or-√b 2 -4ac 2a an example of how it is used: X 2 -4x-12=0 the coefficient of x 2 is 1 therefore the value of A=1 the coefficient of -3x is -3 therefore B is equal to -3 and the number with no variable is the C value, which is -7. now we need to find the discriminant the discriminant will tell us the number and type of answer we will get. We can find the discriminant by using the formula b 2 -4ac and using the values found previously for a,b and c. After we plug in all of the values and simplify we find that x is equal to 4+or-√32

To solve using completing the squares you first take a quadratic equation such as x 2 -6x+2=0 and divide the coefficient of the x variable by 2. you then square the quotient and whatever that equals which in this case is 9. You subtract the 2 from both sides and then subtract the 9 from both sides. When all of these modifications are complete the equation will look like this “x 2 -6x-9=-11” after you have this modeled you take the quotient of the coefficient of the x variable divided by 2 and but it into another formula, which is (x-3(the quotient))(x-3)=-11( the sum of -2 and -9) you shorten this by putting it in this form “√(x-3) 2 =√-11” the square root and squared cancel each other out and leave you with “x-3= √-11” you then solve like a normal equation, add three to both sides then change √-11 to √11i since there can be no negative roots, and the answer will be √-11+3

First you take an equation such as x2+6x=-8 and set it equal to zero. You do this by adding 8 to both sides. The outcome will be x2+6x+8=0. you then have to find two numbers that add to 6(or any value in the position of 6) but also multiply to 8(or any value in the position of 8) the two numbers for this are 4 and 2. you than set them up as shown, “x+4=0 and x+2=0” you then solve like any equation subtracting from both sides or adding if it is a negative value. The x values for this quadratic equation are x=-4 and x=-2.

To solve by graphing you need a graphing calculator or a printed out graph. To find the values of x, you use the x-intercept of the graph and wherever the y- intercept equals zero the x-intercept that corresponds with it is the value of x. As an example, if you graphed the function f(x)= x 2 – 8x + 15 the solution of x would be 3 and 5.