{"id":1547,"date":"2019-01-12T06:58:03","date_gmt":"2019-01-12T06:58:03","guid":{"rendered":"https:\/\/kellyfish.me\/?p=1547"},"modified":"2019-01-12T07:00:02","modified_gmt":"2019-01-12T07:00:02","slug":"parabolas","status":"publish","type":"post","link":"https:\/\/kellyfish.me\/index.php\/2019\/01\/12\/parabolas\/","title":{"rendered":"Parabolas"},"content":{"rendered":"

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Fun Math for Girls
\nBy Kelly Tan<\/span><\/span><\/p>\n

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Playing ball games with your friends can be fun, but do you know how a volleyball, basketball, or even a ping pong ball travels in the air?<\/span><\/p>\n

When you throw a ball into the air, it will travel in an arc-shape. This arc is called a <\/span>parabola<\/span><\/i>, which you may have noticed, looks something like this:<\/span><\/span><\/p>\n

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A <\/span>parabola<\/span><\/i> is a curve where any point on the curve is an equal distance from: a point called the <\/span>focus<\/span><\/i>, and a line called the <\/span>directrix<\/span><\/i>.<\/span><\/span><\/p>\n

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The general equation for a parabola is $y = ax^2 + bx + c$, where the $a, b, c$ coefficients can change. Here is what each coefficient does to the parabola:<\/span><\/span><\/p>\n

a<\/span><\/i> makes the parabola wider or thinner
\n<\/span><\/span>c<\/span><\/i> moves the parabola up or down (along the y axis), without changing the shape
\n<\/span><\/span>b<\/span><\/i> is a little more complicated. As the <\/span>b<\/span><\/i> coefficient changes, the shape of the parabola stays the same. Unlike <\/span>c<\/span><\/i>, however, the parabola doesn\u2019t move up and down, or left and right either. Instead, it traces the path of another separate parabola. This may be confusing, so you can watch the video below. Notice how the tip of the orange parabola is always following the green parabola.<\/span><\/span><\/p>\n

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