![finding the vertex of a quadratic function finding the vertex of a quadratic function](https://i.ytimg.com/vi/v4Xg2M9oP4w/maxresdefault.jpg)
Compare the given equation with the standard form (y = ax 2 + bx + c) and get the values of a,b, and c.If the above processes seem difficult, then use the following steps: Which method is easier? Decide and go ahead. Note that we have got the same answer as in the other method. Substitute these two values (along with a = -3) in the vertex form y = a (x - h) 2 + k, we get y = -3 (x + 1) 2 - 6. Comparing this equation with y = ax 2 + bx + c, we get a = -3, b = -6, and c = -9.
![finding the vertex of a quadratic function finding the vertex of a quadratic function](https://i.pinimg.com/736x/eb/20/a6/eb20a6e064119329c3bece3d50ca3f57--step-by-step-guide-quadratic-function.jpg)
Let us convert the same example y = -3x 2 - 6x - 9 into standard form using this formula method. Just use this to find k by substituting the value of 'h' from the above step. Since (h, k) lies on the given parabola, k = ah 2 + bh + c.But the values of h and k can be easily found by using the following steps: In the above method, ultimately we could find the values of h and k which are helpful in converting standard form to vertex form. This is of the form y = a (x - h) 2 + k, which is in the vertex form. Step 5: Simplify the last two numbers and distribute the outside number. The above expression from Step 3 becomes: Here, we can use x 2 + 2xy + y 2 = (x + y) 2. Step 4: Factorize the perfect square trinomial formed by the first 3 terms using the suitable identity. Step 3: Add and subtract the above number after the x term in the expression.
![finding the vertex of a quadratic function finding the vertex of a quadratic function](https://i.pinimg.com/originals/c3/7e/0b/c37e0b8af9749d6bcc3c0ac8d5e315d6.jpg)
Step 2: Make it half and square the resultant number. Here are the steps to convert the above expression into the vertex form. If the coefficient of x 2 is NOT 1, we will place the number outside as a common factor. First, we should make sure that the coefficient of x 2 is 1. Let us take an example of a parabola in standard form: y = -3x 2 - 6x - 9 and convert it into the vertex form by completing the square. But apart from this, we have a formula method also for doing this. So to convert the standard form to vertex form, we just need to complete the square. In the vertex form, y = a (x - h) 2 + k, there is a "whole square".
#Finding the vertex of a quadratic function how to
How to Convert Standard Form to Vertex Form?