How do I sketch interperate and graph a quadratic

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quadratic eqn: y = ax^2 +bx + c

when a>0, the curve is u-shaped. when a<0, the curve is inverted u-shaped. c is the y-intercept.

let y=0 to find the solutions of x, (x1 and x2). thus you will get 2 points on the graph, (x1,0) and (x2,0)

the line of symmetry is the imaginary line that passes through the minimum/maximum point of the curve. to find the minimum/maximum point, (x1+x2)/2 gives the x value (x3). sub x3 into the eqn, you get the y value (y1). so the point is (x3,y1).

using these points you can draw the graph, or you can also sub in other values of x to get a more detailed graph

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