In this situation, the solution of -2 doesn’t make sense. ![]() We know our mathematical solutions are \(x=-2\) and \(x=4\). In function terms, this means “on the \(x\)-axis.” In this situation, that means “on the ground.” This is the function \(f(x)=-x^ +2x + 8 = 0\), which we have already done many times over. In other words, the solutions to a quadratic equation are the values that make the quadratic function true when \(f(x)=0\) or \(y=0\). So instead of the function \(f(x)=ax^2+bx+c\), we write the related equation: \(0=ax^2+bx+c\). So what do we mean by “solving”? In this case, one of the things it means is to figure out which values of the variable, if any, make the equation 0. Now that we have a little background, let’s dive further into solving quadratic equations and interpreting the results. The different characteristics of quadratic functions that are most commonly analyzed are the vertex (the maximum or minimum point), the x-intercepts (the zeros), and the axis of symmetry. ![]() When we graph quadratic functions, we’ll notice that they can be used to tell all kinds of visual stories, from a daredevil shooting out of a cannon to a satellite dish listening to interstellar signals.Įquations for these functions generally look like this: \(f(x)=ax^2+bx+c\) and their graphs form a characteristic shape called a parabola, which looks something like this one: ![]() Hi, and welcome to this overview of quadratic equations! Before we dive into how to solve them, let’s first talk about quadratic functions.
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