finding the vertex of a quadratic function

FINDING THE VERTEX OF A QUADRATIC FUNCTION HOW TO

Then, we plug in x = c into the function f(x) to find the y-coordinate of the vertex (we’ll call it d). We calculate c = (r + s) / 2 to find the x-coordinate of the vertex. To find the vertex of a quadratic function in factored form, we take the average of the zeros.

FINDING THE VERTEX OF A QUADRATIC FUNCTION HOW TO

How To Find The Vertex Of A Quadratic Function In Factored Form So, the zeros of the function are r = -7 and s = -9. Here, we can see that a = 5, r = -7, and s = -9. Example 2: Finding The Zeros Of A Quadratic Function In Factored Formĭon’t be too hasty and make a mistake! We should rewrite (x + 7) as (x – (–7)) and (x + 9) as (x – (–9)): So, the zeros of the function are r = 3 and s = 5. The graph of the function f in the xy-plane above is a parabola. Here, we can see that a = 2, r = 3, and s = 5. Let’s say our quadratic function in factored form is: Example 1: Finding The Zeros Of A Quadratic Function In Factored Form Let’s look at some examples to make sure the concept is clear. This information is helpful when graphing the corresponding parabola. This tells us that f(r) = 0 and f(s) = 0. To find the zeros of a quadratic function in factored form, find the x values that will make the expression inside each set of parentheses equal to zero. How To Find The Zeros Of A Quadratic Function In Factored Form Let’s take a look at some examples to show how to do all of these things (finding the zeros, finding the vertex, and graphing the parabola). It is easy to find points to start graphing the corresponding parabola (use the vertex as a base, and use the zeros if the function has them).

It is easy to find the vertex of the corresponding parabola (the x-coordinate is the average of r and s).

It is easy to find the zeros of the function in this form (they are x = r and x = s).

Quadratic factored form is useful for several reasons: (You can get a refresher on quadratic functions and the 3 forms in my article here). Note that the a in the quadratic factored form is the same one as in standard form of a quadratic:

Finding the vertex of a quadratic function