Quadratic equations are equations in the format ax^2+bx+c. Ax^2 represents the quadratic term, bx represents the linear term, and c is the constant term. The graphs for these equations will always look like a U or an upside-down U.
One way to solve quadratic equations is by graphing. Taking the equation x^2+6x+8 and plugging it in give two solutions, -2 and -4, as shown by the graph below.
Another way to solve quadratic equations is by factoring. Using the same equation, we must find two numbers that can be multiplied together to equal 8 and added together to equal 6. (x+2)(x+4) can be foiled out to check the work, and it equals our original equation. Because this equation is assumed to be set equal to 0, to find what x equals each parenthesis must be set equal to 0. If the first one, x+2, is equal to zero, then subtracting 4 from each side will result in one answer. When x+4=0, x=-4.
The third way to solve quadratic equations is by completing the square. Using the same equation, we first subtract 8 from each side. Then, to complete the square, divide the 6 by 2. Take the quotient, square it, and add the number to each side. Now our equation(x^2+6x+9=-8+9) can be factored out. (x+3)^2=1. Square root each side to get rid of the exponent. Taking the square root of a variable makes it either plus or minus the number, so the equation is x+3=(+or-)1. Now the equation can easily be solved. x+3=1. Subtract 3 from each side and x=-2. In x+3=-1, subtract 3 from each side to get x=-4.
The final method is solving using the equation x=-b(+or-) the square root of b^2-4(a)(c) all over 2a. If a=1, b=6, and c=8, then the equation is x=-6(+or-) the square root of 36-4(1)(8) all over 2(1). Simplify to get x=-6(+or-) the square root of 4 all over 2. The square root of 4 is 2. Everything in the equation is divisible by 2. x=-3(+or-)1. x=-3+1 is -2 and x=-3-1 is -4.
One way to solve quadratic equations is by graphing. Taking the equation x^2+6x+8 and plugging it in give two solutions, -2 and -4, as shown by the graph below.
Another way to solve quadratic equations is by factoring. Using the same equation, we must find two numbers that can be multiplied together to equal 8 and added together to equal 6. (x+2)(x+4) can be foiled out to check the work, and it equals our original equation. Because this equation is assumed to be set equal to 0, to find what x equals each parenthesis must be set equal to 0. If the first one, x+2, is equal to zero, then subtracting 4 from each side will result in one answer. When x+4=0, x=-4.
The third way to solve quadratic equations is by completing the square. Using the same equation, we first subtract 8 from each side. Then, to complete the square, divide the 6 by 2. Take the quotient, square it, and add the number to each side. Now our equation(x^2+6x+9=-8+9) can be factored out. (x+3)^2=1. Square root each side to get rid of the exponent. Taking the square root of a variable makes it either plus or minus the number, so the equation is x+3=(+or-)1. Now the equation can easily be solved. x+3=1. Subtract 3 from each side and x=-2. In x+3=-1, subtract 3 from each side to get x=-4.
The final method is solving using the equation x=-b(+or-) the square root of b^2-4(a)(c) all over 2a. If a=1, b=6, and c=8, then the equation is x=-6(+or-) the square root of 36-4(1)(8) all over 2(1). Simplify to get x=-6(+or-) the square root of 4 all over 2. The square root of 4 is 2. Everything in the equation is divisible by 2. x=-3(+or-)1. x=-3+1 is -2 and x=-3-1 is -4.