For the following exercises, solve the quadratic equation. Also, especially in the beginning, put the b. I teach my students to start with the discriminant, b2-4ac. We always have to start with a quadratic in standard form: ax2+bx+c0. For the following exercises, solve the quadratic equation by completing the square. This is a formula, so if you can get the right numbers, you plug them into the formula and calculate the answer (s). Now we use our algebra skills to solve for "x". For the following exercises, solve the quadratic equation by using the square-root property. Total time = time upstream + time downstream = 3 hours (to travel 8 km at 4 km/h takes 8/4 = 2 hours, right?) We can turn those speeds into times using:
Let x = the boat's speed in the water (km/h).There are two speeds to think about: the speed the boat makes in the water, and the speed relative to the land: What is the boat's speed and how long was the upstream journey? The negative value of x make no sense, so the answer is:Įxample: River Cruise A 3 hour river cruise goes 15 km upstream and then back again. The desired area of 28 is shown as a horizontal line. Check your answers when you are finished with each question. There are many ways to solve it, here we will factor it using the "Find two numbers that multiply to give ac, and add to give b" method in Factoring Quadratics: Answer the following questions pertaining to quadratic inequalities. It looks even better when we multiply all terms by −1: (Note for the enthusiastic: the -5t 2 is simplified from -(½)at 2 with a=9.8 m/s 2)Īdd them up and the height h at any time t is:Īnd the ball will hit the ground when the height is zero: Gravity pulls it down, changing its position by about 5 m per second squared:
It travels upwards at 14 meters per second (14 m/s): (Note: t is time in seconds) The height starts at 3 m: Ignoring air resistance, we can work out its height by adding up these three things: