Solving Quadratic Equation Word Problems

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Need help figuring out how to unpack and solve word problems involving quadratic equations? From Ramanujan to calculus co-creator Gottfried Leibniz, many of the world's best and brightest mathematical minds have belonged to autodidacts.

And, thanks to the Internet, it's easier than ever to follow in their footsteps (or just finish your homework or study for that next big test).

TRACE (CALC), 4 (maximum), moved the cursor to the left of the top after “Left Bound? ” move the cursor anywhere to the right of that zero and hit ENTER. Height versus distance would be the path or trajectory of the bouquet, as in the following problem.

”, moved the cursor to the right of the top after “Right Bound? To get the root, push 2 TRACE (CALC), and then push 2 for ZERO (or move cursor down to ZERO). ” Using the cursors, move the cursor anywhere to the left of the zero (where the graph hits the \(x\)-axis) and hit ENTER. Audrey throws a ball in the air, and the path the ball makes is modeled by the parabola \(y-8=-0.018\), measured in feet.

The smaller value is the length of the shorter leg and the higher value is the hypotenuse of the right triangle.

Quadratic applications are very helpful in solving several types of word problems (other than the bouquet throwing problem), especially where optimization is involved.Note also that we will discuss Optimization Problems using Calculus in the Optimization section here.where \(t\) is the time in seconds, and \(h\) is the height of the ball.We want to find the ticket price that gives the maximum profit, and also find that maximum profit.Solution: This problem is actually much easier since we are given the formula for the profit, given the price of each ticket.We could expand the binomial and use the quadratic formula, but it’s much easier to use the square root method, since we have a square in the original: \(\begin0&=-0.018 8\\frac&=\\pm \sqrt&=\sqrt\x-20&=\pm 21.08\x&=41.08\end\) Note that we had to “throw away” the negative part of the solution.The ball will hit the ground feet of fencing How is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, volunteer authors worked to edit and improve it over time. Typically a reasonable range for these types of problems is The profit from selling local ballet tickets depends on the ticket price.Using past receipts, we find that the profit can be modeled by the function \(p=-15 600x 60\), where \(x\) is the price of each ticket.


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