We can then form 3 equations in 3 unknowns and solve them to get the required result. To find the unique quadratic function for our blue parabola, we need to use 3 points on the curve. ![]() So how do we find the correct quadratic function for our original question (the one in blue)? System of Equations method It turns out there are an infinite number of parabolas passing through the points (−2,0) and (1,0).Īnd don't forget the parabolas in the "legs down" orientation: Let's substitute x = 0 into the equation I just got to check if it's correct. Observe my graph passes through −3 on the y-axis. This is a quadratic function which passes through the x-axis at the required points. Now, we can write our function for the quadratic as follows (since if we solve the following for 0, we'll get our 2 intersection points): X = 1 (since the graph cuts the x-axis at x = 1.) X = −2 (since the graph cuts the x-axis at x = − 2) and ![]() We can see on the graph that the roots of the quadratic are: (We'll assume the axis of the given parabola is vertical.) Parabola cuts the graph in 2 places Sometimes it is easy to spot the points where the curve passes through, but often we need to estimate the points. Our job is to find the values of a, b and c after first observing the graph. We know that a quadratic equation will be in the form: The parabola can either be in "legs up" or "legs down" orientation. The graph of a quadratic function is a parabola. (Most "text book" math is the wrong way round - it gives you the function first and asks you to plug values into that function.) A quadratic function's graph is a parabola ![]() Often we have a set of data points from observations in an experiment, say, but we don't know the function that passes through our data points. This is a good question because it goes to the heart of a lot of "real" math. I would like to know how to find the equation of a quadratic function from its graph, including when it does not cut the x-axis.
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