lesson
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If you drive a car at a steady speed, your distance grows in a straight line. But if you stomp on the gas pedal, you accelerate โ and the distance you cover begins to curve upward dramatically.
This curved relationship is modeled by a quadratic function, one of the most useful tools in all of algebra for describing motion, gravity, and area.
What Makes an Equation Quadratic?
A quadratic function is any function whose highest exponent (or degree) on the variable is 2.
Its standard form is written as y=ax2+bx+c, where a, b, and c are numbers and a๎ =0.
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If a=0, the x2 term vanishes and the function collapses into a linear equation (y=bx+c). That is why the squared term is the defining heartbeat of every quadratic.
Spotting Quadratics in Disguise
Sometimes an equation is quadratic even if it does not look like standard form at first glance. You may need to expand brackets or rearrange terms to reveal the highest power.
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Equations are straightforward to inspect โ but what if you are only given a table of raw data points? How can you tell if the underlying pattern is quadratic?
The Second Differences Test
In a linear function, the y-values change by the exact same amount for every step of x. This constant jump is called the first difference.