How To Solve — Quadratic Word Problems Grade 10

If the question asks for a maximum or minimum (e.g., "What is the greatest area?"), completing the square is often the fastest method because it gives you the vertex $(h, k)$, which is the max/min.

: Use given conditions to create an equation in terms of Simplify to Standard Form : Rearrange the equation into

18x - x² = 77 → Bring all terms to one side: 0 = x² - 18x + 77 So x² - 18x + 77 = 0 . Factor: (x - 7)(x - 11) = 0 → x = 7 or x = 11 . how to solve quadratic word problems grade 10

A theater sells tickets for $10. At this price, 300 tickets are sold. For every $1 increase in price, 20 fewer tickets are sold. What price maximizes revenue?

A farmer has 40 meters of fencing to enclose three sides of a rectangular garden (the fourth side is against a barn and needs no fencing). What dimensions will maximize the area of the garden? If the question asks for a maximum or minimum (e

Quadratic word problems are best solved using a step-by-step strategy:

[ x = \frac-b \pm \sqrtb² - 4ac2a ] Example: ( 2w² + 3w - 50 = 0 ) ( a = 2, b = 3, c = -50 ) [ w = \frac-3 \pm \sqrt9 - 4(2)(-50)4 = \frac-3 \pm \sqrt4094 ] ( \sqrt409 \approx 20.22 ) ( w \approx 4.305 ) or ( w \approx -5.805 ) (ignore negative for width) A theater sells tickets for $10

Don't reinvent the wheel for every question. Use this four-step process to keep your thoughts organized.

This is the most critical step in word problems.

If you are in Grade 10, you have likely encountered the dreaded "quadratic word problem." They often sound like this: "A ball is thrown into the air..." or "A rectangular garden has a path of uniform width..."