2-3: Solving 2-3: Solving Quadratic Equations Quadratic Equations

by Factoringby Factoring

2-3: Solving 2-3: Solving Quadratic Equations Quadratic Equations

by Factoringby FactoringUnit 2 Unit 2

English CasbarroEnglish Casbarro

Warm-up Problems1. Your friend attempted to factor an expression as shown to the right. Find the error in your friend’s work. Then factor the expression correctly.

2. The area in square feet of a rectangular field is x2 – 120x + 3500. The width, in feet, is x – 50. What is the length in feet?

3. The volume of a cylinder is given by the formula, V = πr2 h. What is the volume of the shaded pipe with outer radius R, inner radius r, and height h as shown? Express your answer in completely factored form.

4. A tee box is 48 feet above the fairway. Starting with an initial elevation of 48 ft. at the tee box and an initial velocity of 32 ft/s, the quadratic equation 0 = –16t2 + 32t + 48 gives the time t in seconds when a golf ball is at height 0 on the fairway.

a. Solve the quadratic equation by factoring to see how long the ball is in the air. b. What is the height of the ball at 1 second? c. Is the ball at its maximum height at 1 second? Explain.

You can always graph the equation to check the solutions. If the equationwill factor, then you should be able to see the solution on a graph.

There are alternative methods using a graphing calculator. One uses theTable feature (over the Graph button).

Another uses the Zero function in the Calc feature.

Real-life problemsAn object is dropped from a height of 1700 ft. above the ground. The function h = –16t2 + 1700 gives the object’s height h in feet during thefree fall at t seconds.

a. When will the object be 1000 ft. above the ground?b. When will the object v=be 940 ft. above the ground?c. What are the reasonable domain and range for the function h?

Equations in Quadratic Form

Now, once you have factored the equation in quadratic form, you canfind solutions to the equation.

Turn in the following problems

1. Write an equation that could be used to find two consecutive even integers whose sum is 24. Let x represent the first integer. Solve the equation and give the 2 integers.

2. One base of a trapezoid is the same length as the height of the trapezoid. The other base is 4 cm. more than the height. The area of the trapezoid is 48 cm2. Find the length of the shorter base. (Hint: Use A = ½h(b1 + b2). )

3.