Question

Learning Task 2. Solve each problem using quadratic functions.
1. The sum of two positive integers is 35. What is the minimum sum of their
squares?
2. A rectangle has a perimeter of 100 cm. Find the greatest possible area for
the rectangle.​

Answer 1

Answer:

The sum of two consecutive odd numbers is −100. Find the numbers.

If you missed this problem, review (Figure).

Solve: \frac{2}{x+1}+\frac{1}{x-1}=\frac{1}{{x}^{2}-1}.

If you missed this problem, review (Figure).

Find the length of the hypotenuse of a right triangle with legs 5 inches and 12 inches.

If you missed this problem, review (Figure).

Solve Applications Modeled by Quadratic Equations

We solved some applications that are modeled by quadratic equations earlier, when the only method we had to solve them was factoring. Now that we have more methods to solve quadratic equations, we will take another look at applications.

Let’s first summarize the methods we now have to solve quadratic equations.

Methods to Solve Quadratic Equations

Factoring

Square Root Property

Completing the Square

Quadratic Formula

As you solve each equation, choose the method that is most convenient for you to work the problem. As a reminder, we will copy our usual Problem-Solving Strategy here so we can follow the steps.

Use a Problem-Solving Strategy.

Read the problem. Make sure all the words and ideas are understood.

Identify what we are looking for.

Name what we are looking for. Choose a variable to represent that quantity.

Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebraic equation.

Solve the equation using algebra techniques.

Check the answer in the problem and make sure it makes sense.

Answer the question with a complete sentence

Step-by-step explanation:

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