A quadratic equation is any equation of the form y = ax^2 + bx + c (or could be written this way). A parabola is the shape of the graph of that equation.
There are a lot of details to learn about but above is all there is to know to start. You’ll deal with different parts of this through calculus.
The graph is a “U” shape either with a lowest point (if right up) or highest point (if upside down). They are symmetrical left-right. The values a, b, c determine how wide and flat or tall and skinny and where that middle point is.
Good practice is just to pick some numbers a, b, c then make a table from say -10 to +10 and calculate what y= for those 21 values. Then put those 21 points on graph paper and connect them with a curve.
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