How to Find Quadratic Functions From a Graph Not Crossing the X Axis

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Finding quadratic functions from a graph that does not cross the X axis will require you to take a closer look at the parabola. Find the quadratic functions from a graph that does not cross the X axis with help from an experienced math professional in this free video clip.

Part of the Video Series: Solving Math Problems
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Video Transcript

Hi, I'm Ryan Ault. I'm a physicist, and this is how to find quadratic functions for a graph not crossing the X axis. If we look up here we see that the graph parabola is not crossing the X axis and two points are labeled, the vertex at 2, 1 and some other random point. In this case it's 3, 4. So the first thing we can do is write down what each variable in this equation is and how it relates to these points. Now the vertex is actually defined by V of 2, 1 which is equal to V of H and K. So in this case H is equal to 2 and K equals 1. Now, the next step is to identify what this point actually means here, so 3 and 4. What this implies is that F of X which is equal to 3, is equal to the Y value, 4. Okay so now we can go down to this equation and we find that F of X which is in our case, when X equals 3, is 4 which equals A times X minus H which is 2 squared plus K which is 1. Now we also know that X equals 3 and this whole term right here just becomes 1 squared. So this is simply A times 1 plus 1 equals 4 and we can solve for A by subtracting 1 from both sides and we find that 3 is equal to A. Now we can rewrite this whole equation using our value of A and we find that F of X is equal to 3 times X minus 2 squared plus 1. Here, we have the equation for a quadratic. It does not cross the X axis. I'm Ryan Ault and this is find the quadratic equation for a function not crossing the X axis.

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