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It means you are required to "solve" a quadratic equation by factorising the quadratic equation into two binomial expressions. Solving means to find the value(s) of the variable for which the expression equals zero.
That doesn't factor neatly. Applying the quadratic formula, we find two real solutions: -2 plus or minus the square root of 6. x = 0.4494897427831779 x = -4.4494897427831779
That doesn't factor neatly. Applying the quadratic formula, we find two real solutions: (-1 plus or minus the square root of 901) divided by 2. x = 14.508331019803634 x = -15.508331019803634
That doesn't factor neatly. Applying the quadratic formula, we find two real solutions: (5 plus or minus the square root of 73) divided by 12. y = 1.128666978776461 y = -0.2953336454431275
If that were x^2 - 3x - 4, it would be (x + 1)(x - 4) As it is, it doesn't factor neatly. Applying the quadratic formula, we find two real solutions. (3 plus or minus the square root of 41) divided by two. x = 2.350781059358212 x = -0.8507810593582121
The vertex must be half way between the two x intercepts
There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
Graph the equation then find the x intercepts.
In general, quadratic equations have graphs that are parabolas. The quadratic formula tells us how to find the roots of a quadratic equations. If those roots are real, they are the x intercepts of the parabola.
The general form of a quadratic equation is ax^2+bx+c=0. The quadratic formula is used to find the x intercepts of a parabola. It goes like this: x=(-b+or-the (square root of b^2-4ac))/2a. With a specific equation you plug the values for a, b, and c into the formula. It is best to use a graphing calculator. Hope this helps.
To find the roots (solutions) of a quadratic equation.
When an equation cannot be solved for "x" to find the zeroes, the quadratic formula can be used instead for the same purpose.
I suggest you use the quadratic formula.
the formula you are going to use to answer the equation
To find the solutions of x in a quadratic equation.
The quadratic formula can be used to find the solutions of a quadratic equation - not a linear or cubic, or non-polynomial equation. The quadratic formula will always provide the solutions to a quadratic equation - whether the solutions are rational, real or complex numbers.
Plug 'a', 'b', and 'c' from the equation into the formula. When you do that, the formula becomes a pair of numbers ... one number when you pick the 'plus' sign, and another number when you pick the 'minus' sign. Those two numbers are the 'solutions' to the quadratic equation you started with.