That is, if the parabola has indeed two real solutions. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. We know this even before plotting "y" because the coefficient of the first term, 3 , is positive (greater than zero).Įach parabola has a vertical line of symmetry that passes through its vertex. Our parabola opens up and accordingly has a lowest point (AKA absolute minimum). Parabolas have a highest or a lowest point called the Vertex. let us now solve the equation by Completing The Square and by using the Quadratic Formula Parabola, Finding the Vertex : Supplement : Solving Quadratic Equation Directly Solving 3x 2-5x-8 = 0 directlyĮarlier we factored this polynomial by splitting the middle term. Subtract 1 from both sides of the equation : In other words, we are going to solve as many equations as there are terms in the productĪny solution of term = 0 solves product = 0 as well. We shall now solve each term = 0 separately When a product of two or more terms equals zero, then at least one of the terms must be zero. Which is the desired factorization Equation at the end of step 2 : (3x - 8) ģ.1 A product of several terms equals zero. Step-5 : Add up the four terms of step 4 : Step-4 : Add up the first 2 terms, pulling out like factors :Īdd up the last 2 terms, pulling out common factors : Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 3 Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is -5. Step-1 : Multiply the coefficient of the first term by the constant 3 The middle term is, -5x its coefficient is -5. The first term is, 3x 2 its coefficient is 3. Step 2 : Trying to factor by splitting the middle term ![]() Step by step solution : Step 1 : Equation at the end of step 1 : (3x 2 - 5x) - 8 = 0 ![]() Changes made to your input should not affect the solution:
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