# Solve The Quadratic Equation Word Problems Worksheet

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Solve the quadratic equation word problems means using math to solve real-life situations described in words. We turn the story into a math problem $$ax^2 + bx + c = 0$$, find $$a$$, $$b$$, and $$c$$, and then use methods like factoring or the quadratic formula x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} to find the solutions. It helps us practice math skills and apply them to everyday problems.

Algebra 2

## How Will This Worksheet on “Solve the Quadratic Equation Word Problems” Benefit Your Student's Learning?

• It uses math to solve everyday problems, making learning more meaningful.
• Students figure out problems, find what they need to solve, and use the right way to solve them.
• Solving quadratic equations teaches ways like breaking down and using the quadratic formula.
• Learning quadratic equations helps with harder math, like calculus.
• Knowing quadratic equations is important for jobs that use math to study and solve problems.

## How to Solve the Quadratic Equation Word Problems?

• First, understand the scenario and identify the unknowns that need to be solved.
• Use the information given to set up a quadratic equation in the form $$ax^2 + bx + c = 0$$.
• Decide whether to solve by factoring, completing the square, or using the quadratic formula x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
• Then, calculate the values of $$x$$ using the chosen method and interpret them in the context of the problem to find the solution(s).

## Solved Example

Q. For his school's annual egg-drop contest, Nick created a cushioned egg container made of cotton balls and tin foil. In the first round, Nick dropped his egg from the school's second floor balcony $18$ feet above the ground, and the egg survived!$\newline$$\newline$If an object is dropped from $s$ feet above the ground, the object's height in feet, $h$, $t$ seconds after being dropped can be modeled by the formula $h = -16t^2 + s$.$\newline$To the nearest tenth of a second, how long did it take for the egg to hit the ground?$\newline$$\_\_\_$ seconds$\newline$
Solution:
1. Given: If an object is dropped from $s$ feet, its height $h$ after $t$ seconds can be modeled by the formula: $h = -16t^2 + s$.$\newline$ Since the egg hits the ground, $h = 0$. And has an initial height of $s=18$ feet.$\newline$ So, the correct equation is: $\newline$$0 = -16t^2 + 18$
2. Solve for $t$: Solve the equation $0 = -16t^2 + 18$ for $t$.$\newline$ $0 = -16t^2 + 18$$\newline$ $-16t^2 = -18$$\newline$ Divide both sides by $-16$.$\newline$ $t^2 =\frac{18}{16}$ $t^2 = 1.125$
3. Take Square Root: Take the square root of both sides to solve for $t$. $\newline$$t = \sqrt{1.125}$ $t \approx 1.06$
4. Round to Nearest Tenth: Round to the nearest tenth. $t \approx 1.1$ seconds

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