How to write a quadratic function in standard form with given zeros

I know they're all called f, but we're gonna just assume they are different functions. Well, when t is equal to five, five minus five squared is just zero. Make sure we see that, so this is negative one right over here, negative one.

So factored form is definitely what you want when you're trying to find the zeros. Parabolas have two equation forms — standard and vertex.

quadratic equation calculator

So it's not too hard to figure out, but there's going to be some calculation in my head. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

quadratic equation calculator

The steps that we use in this section for completing the square will look a little different, because our chief goal here is not solving an equation. These functions were just written in different ways.

quadratic function with zeros calculator

So, we could say t What is f of five? But here for this last one, and this is known as standard form, if I say x equals zero that term disappears, that term disappears and I'm just left with m of zero is equal to negative

Finding polynomial equations with given zeros calculator

Let's see what's possible. So be very, very careful. Because they may have divided something out when they solved the original quadratic. To find the zeros of f, we set f equal to 0 and solve for x. Conclusion: Working backward will create an equation, but remember that there are other equations that will also have that same set of solutions. Any quadratic function can be rewritten in standard form by completing the square. And so what x values make or which one is easy to figure out when this function is equal to zero? These functions were just written in different ways. There you have it. Parabolas have two equation forms — standard and vertex. Let's do one more.
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How do I write a quadratic function when only given the zeros?