STANDARD FORM QUADRATIC EQUATION PLUS

To find the vertex, set x = -h so that the squared term is equal to 0, and set y = k. You can now reformat your quadratic equation into a new formula, a(x + h)^2 + k = y. Subtract 5 from both sides of the equation to get 3(x + 1)^2 – 5 = y. Finally, factor the left side of the equation to get 3(x + 1)^2 = y + 5. In our example, this will give you 3(x^2 + 2x + 1) = y + 2 + 3(1), which you can simplify to 3(x^2 + 2x + 1) = y + 5. Also add the result to the inside of the parentheses on the left side. Multiply the result by the coefficient of the a-term and add the product to the right side of the equation. Now, plug the coefficient of the b-term into the formula (b/2)^2. Then, factor out the coefficient of the first term to get 3(x^2 + 2x) = y + 2. The general form of the quadratic equation is ax+bx+c0 which is always put equals to zero and here the value of x is always unknown, which has to be determined by applying the quadratic formula while the value of a,b,c coefficients is always given in the question. Add 2 to both sides to get the constant out of the way. For example, say you are trying to find the vertex of 3x^2 + 6x – 2 = y.

STANDARD FORM QUADRATIC EQUATION PLUS

This involves re-expressing the equation in the form of a perfect square plus a constant, then finding which x value would make the squared term equal to 0. You can also figure out the vertex using the method of completing the square. Parabolas with a negative a-value open downward, so the vertex would be the highest point instead of the lowest. For this particular equation, the vertex is the lowest point, since the a-value is greater than 0. Describe the vertex by writing it down as an ordered pair in parentheses, or (-1, 3). So, the x-value of the vertex is -1, and the y-value is 3. Once you have the x value of the vertex, plug it into the original equation to find the y value. Plug the a and b values into the vertex formula to find the x value for the vertex, or the number you’d have to input into the equation to get the highest or lowest possible y. So, if you’re working with the equation 2x^2 + 4x + 9 = y, a = 2, b = 4, and c = 9. If your equation is in the form ax^2 + bx + c = y, you can find the x-value of the vertex by using the formula x = -b/2a. The easiest way to find the vertex is to use the vertex formula. If you’re looking at a graph, the vertex would be the highest or lowest point on the parabola. The vertex of the graph of a quadratic function is the highest or lowest possible output for that function.

Standard form quadratic equation