A quadratic equation is an equation that takes the form ax2+bx+c=0{\displaystyle ax^{2}+bx+c=0}. A quadratic equation has two solutions, which means a line written in this form is a parabola and will have two x-intercepts. For example, the equation x2+3x−10=0{\displaystyle x^{2}+3x-10=0} is a quadratic equation, so this line will have two x-intercepts. The formula is x=−b±b2−4ac2a{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}, where a{\displaystyle a} equals the coefficient of the second-degree term (x2{\displaystyle x^{2}}), b{\displaystyle b} equals the coefficient of the first-degree term (x{\displaystyle x}), and c{\displaystyle c} equals the constant. Make sure you substitute the correct values for each variable from the equation of the line. For example, if the equation of your line is x2+3x−10=0{\displaystyle x^{2}+3x-10=0}, your quadratic formula will look like this: x=−3±32−4(1)(−10)2(1){\displaystyle x={\frac {-3\pm {\sqrt {3^{2}-4(1)(-10)}}}{2(1)}}}. To do this, first complete all of the multiplication. Make sure you pay close attention to all positive and negative signs. For example:x=−3±32−4(−10)2(1){\displaystyle x={\frac {-3\pm {\sqrt {3^{2}-4(-10)}}}{2(1)}}}x=−3±32+402{\displaystyle x={\frac {-3\pm {\sqrt {3^{2}+40}}}{2}}} Square the b{\displaystyle b} term. Then, add this number to the other number under the square root sign. For example:x=−3±32+402{\displaystyle x={\frac {-3\pm {\sqrt {3^{2}+40}}}{2}}}x=−3±9+402{\displaystyle x={\frac {-3\pm {\sqrt {9+40}}}{2}}}x=−3±492{\displaystyle x={\frac {-3\pm {\sqrt {49}}}{2}}} Since the quadratic formula has a ±{\displaystyle \pm }, you will solve once by adding, and once by subtracting. Solving by adding will give you your first x{\displaystyle x} value. For example:x=−3+492{\displaystyle x={\frac {-3+{\sqrt {49}}}{2}}}x=−3+72{\displaystyle x={\frac {-3+7}{2}}}x=42{\displaystyle x={\frac {4}{2}}}x=2{\displaystyle x=2} This will give you the second value for x{\displaystyle x}. First calculate the square root, then find the difference in the numerator. Finally, divide by 2. For example:x=−3−492{\displaystyle x={\frac {-3-{\sqrt {49}}}{2}}}x=−3−72{\displaystyle x={\frac {-3-7}{2}}}x=−102{\displaystyle x={\frac {-10}{2}}}x=−5{\displaystyle x=-5} Remember that an ordered pair gives the x-coordinate first, then the y-coordinate (x,y){\displaystyle (x,y)}. The x{\displaystyle x} values will be the values you calculated using the quadratic formula. The y{\displaystyle y} value will be 0, since at the x-intercept, y{\displaystyle y} always equals 0. For example, for the line x2+3x−10=0{\displaystyle x^{2}+3x-10=0}, the x-intercepts are at points (2,0){\displaystyle (2,0)} and (−5,0){\displaystyle (-5,0)}.

Summary: Determine that the equation of the line is a quadratic equation. Set up the quadratic formula. Plug all of the values into the quadratic formula. Simplify the equation. Calculate the exponent. Solve for the addition formula. Solve for the subtraction formula. Find the ordered pairs for the x-intercept.


The exact weight you should start with depends on how much weight-training experience you have and the size and weight of your body. The more experience you have lifting weights, the heavier kettlebell you can start with. Even if you’re an experienced weightlifter, you may want to start with a lighter kettlebell until you get used to exercising with it. Regular cast iron kettlebells have bigger handles that you can grab onto with 2 hands, which is helpful when you first start exercising with them. Avoid using competition kettlebells, which have smaller handles that can only be gripped with 1 hand. It’s important that you know how to grip a kettlebell correctly so you don’t injure yourself. There are a variety of ways you can hold a kettlebell, and the grip you should use depends on the exercise you’re doing. Some common grips are:  Single-handed grip: Wrap your fingers around the handle on the kettlebell so your palm is facing in toward your body. Double-handed grip: The same as a single-handed grip, but with both hands. Goblet: Hold the kettlebell at your chest so each of your hands is gripping a side of the handle. Keep your elbows tucked in at your sides. Racked: Grip the kettlebell with 1 hand and hold it up near your chest so the bulk of the kettlebell is resting on your forearm. Tuck your elbow in at your side. If you’re new to using kettlebells, you’ll want to perfect your form before you move on to heavier weights. Start by practicing kettlebell exercises with light weights. When you get the form down and you feel confident with the motions, then you can progress to heavier weights. Stand up with your feet shoulder width apart, holding the kettlebell in one hand. Move the kettle bell from hand to hand in a circle around your body, while keeping your core as stable as possible.  Start slow with a light kettlebell to get used to changing hands. You may drop your kettlebell a few times as you get used to the motion. Aim for 4 sets of 20 reps each.
Summary: Start with a kettlebell that weighs 15–25 pounds (6.8–11.3 kg). Exercise with a regular cast iron kettlebell when you’re starting out. Practice the different ways of holding a kettlebell before your workout. Progress slowly so you don’t injure yourself. Try Around-the-Worlds to warm up with your kettlebell.