The possible x-values will be the x-intercepts where you line crosses the x-axis. In an equation like a x 2 + b x + c = y, set y = 0and work out the equation. The ever-reliable Quadratic Formula confirms the values of x as - 2 and - 3. Now we can use those in the Quadratic Formula and check, since we already know our answers are - 2 and - 3: We can set each expression equal to 0 and then solve for x:Ĭomparing our example, x 2 + 5 x + 6 = 0, to the standard form of the quadratic equation (which can also just be called “the quadratic”), we get these values: We can see that either expression equals 0 (since multiplying it times the other expression yields 0).
We are seeking two numbers that multiply to 6 and add to 5: Our quadratic equation will factor, so it is a great place to start. ( q u a d r a t i c ) = 0 Solving Quadratic Equations Steps
Let's start with an easy quadratic equation:įor the Quadratic Formula to apply, the equation you are untangling needs to be in the form that puts all variables on one side of the equals sign and 0 on the other: i f b 2 - 4 a c i f b 2 - 4 a c > 0 → 2 s o l u t i o n s.i f b 2 - 4 a c = 0 → 1 s o l u t i o n.The discriminant is used to determine how many solutions the quadratic equation has. The expression b 2 - 4 a c, which is under the (sqrt) inside the quadratic formula is called the discriminant. Or, if your equation factored, then you can use the quadratic formula to test if your solutions of the quadratic equation are correct. You can use this formula to solve quadratic equations. Consider a quadratic equation in standard form: The quadratic formula is used to solve quadratic equations. So a quadratic polynomial has as its highest value something to the second degree something squared. In math, the meaning of square is an exponent to the second degree. But the origin of the word means “to make square,” as in length times width. Confusion enters when we look at the word “quadratic” because it implies four of something, like a quadrilateral. Polynomials (expressions with many terms) can have linear, square, and cubic values. To understand it, to value it, and to apply it correctly, you need to know a tiny bit of its background, then appreciate every term in it. The Quadratic Formula is a milestone along the path to fully understanding algebra. The Quadratic Formula is an algebraic formula used to solve quadratic equations.
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