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    How to Graph a Quadratic Equation: 10 Steps (with …

    How to graph a quadratic equation using a graphing tool?
    We can graph any quadratic equation using a graphing tool. Still, we need to make the graph manually to understand the logic behind its making. Let us consider the simplest quadratic function f (x) = x2. Graphing this on a coordinate plane will give us the shape shown below. Let us consider the most straightforward quadratic function f (x) = x 2.
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    Graphing Quadratic Equations - Math is Fun

    You can graph a Quadratic Equation using the Function Grapher, but to really understandwhat is going on, you can make the graph yourself. Read On!

    Math is Fun

    The simplest Quadratic Equation is: f(x) = x2 And its graph is simple too: This is the curve f(x) = x2 It is a parabola Let us see what happens when we introduce the "a"value: f(x) = ax2 1. Larger values of asquash the curve inwards 2. Smaller values of aexpand it outwards 3. And negative values of aflip it upside down

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    Before graphing we rearrangethe equation, from this: f(x) = ax2+ bx + c To this: f(x) = a(x-h)2+ k Where: 1. h = −b/2a 2. k = f( h ) In other words, calculate h (= −b/2a), then find k by calculating the whole equation for x=h

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    The wonderful thing about this new form is that h and k show us the very lowest (or very highest) point, called the vertex: And also the curve is symmetrical (mirror image) about the axis that passes through x=h, making it easy to graph

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    What if we have a graph, and want to find an equation? Some tips: 1. Plot the axis of symmetry (down the middle) to make sure the graph is symmetrical 2. Double check the direction of the parabola (upward or downward) using the sign of a 3. Plot some extra points to make sure your curve is good

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