These zeros tell us that f(h + √( -k/a)) = 0 and f(h – √( -k/a)) = 0. If a and k have the same signs, then –k/a is negative and we get two complex conjugate roots.If a and k have opposite signs, then –k/a is positive and we get two distinct real roots.If k = 0, we get one repeated real root, x = h. ![]() Note that there are three separate cases for the zeros: ![]() So, we get two zeros for the quadratic function: x = h + √( -k/a) and x = h – √( -k/a). So, we need to find the x values that give us a(x – h) 2 + k = 0. To find the zeros of a quadratic function in vertex form, we need to solve for f(x) = 0. How To Find The Zeros Of A Quadratic Function In Vertex 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 (h, k) as a base, and use the zeros if the function has them, or choose x = 0, f(x) = f(0) = ah 2 + k).It is easy to find the vertex of the corresponding parabola (we just read the values of h and k to get the coordinates (h, k) for the vertex).It is possible to find the zeros of the function from this form with some algebra (by solving the equation for x with f(x) = 0).Quadratic vertex 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 vertex form is the same one as in standard form of a quadratic: Where a is not zero, and (h, k) is the vertex of the parabola. We’ll also look at some examples and answer some common questions about this form. ![]() In this article, we’ll talk about what quadratic vertex form is and what it looks like. Of course, once you are comfortable with the quadratic vertex form, it will be much easier to work with it, graph from it, and convert it to other forms. So, what is quadratic vertex form? A function in quadratic vertex form looks like this: f(x) = a(x – h) 2 + k, where a is not zero and (h, k) is the vertex of the function. This form tells us how high above/below the x-axis the vertex lies (the value of k) and how far left/right of the y-axis the vertex lies (the value of h). A quadratic has 3 different forms, and we can switch between all of them (with a little algebra, of course!) The vertex form of a quadratic is helpful for several reasons, so it helps to know what it is and what it tells you.
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