solving quadratic equations by factoring answer key

#Solving quadratic equations by factoring answer key how to

Maze - Quadratic Functions - Find the Vertex (Given the Vertex Form)Ĥ. Maze - Quadratic Functions - Find the Vertex (Given the Standard Form of QF)ģ.

Maze - Quadratic Functions - Find Axis of SymmetryĢ. On a last note, if you're currently teaching the quadratic unit chapter, 'reviews' of the quadratic bundle has indicated that the following mazes are an awesome resource to use:ġ. This maze could be used as: a way to check for understanding, a review, recap of the lesson, pair-share, cooperative learning, exit ticket, entrance ticket, homework, individual practice, when you have time left at the end of a period, beginning of the period (as a warm up or bell work), before a quiz on the topic, and more. If you're interested in the second level of solving quadratic equation by factoring, you may find it at: Maze - Quadratic Functions - Solve Quadratic Equation by Factoring - Level 2Ī DIGITAL VERSION OF THIS ACTIVITY IS SOLD SEPARATELY AT MY STORE HERE From start to end, the student will be able to answer 17 questions out of the 19 provided to get to the end of the maze. There are 19 quadratic equation provided in this maze. The second level will focus on solving a quadratic equation that must be factored first and is sold separately at my store. Please keep in mind that this maze focuses only on finding the solution of an already factored quadratic equation (level 1). Some roots are integers while others are fractions. Some of the quadratic equations are factored into the product of 2 binomials, others are factored into a binomial squared, while others are factored into the product of a monomial and binomial.

#Solving quadratic equations by factoring answer key how to

This activity is a good review of understanding how to 'Solve Quadratic Equation by Factoring' given the quadratic equation written in 'Factored Form' already (Level 1). Now we use our algebra skills to solve for 'x'.Please check out the collection of mazes which I hope that you find helpful at: 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: when going downstream, v = x+2 (its speed is increased by 2 km/h).

when going upstream, v = x−2 (its speed is reduced by 2 km/h).

Let v = the speed relative to the land (km/h)īecause the river flows downstream at 2 km/h:.

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. Let us solve this one by Completing the Square. How many you sell depends on price, so use 'P' for Price as the variable what is the best price? And how many should you make?

at $350, you won't sell any bikes at all.

$700,000 for manufacturing set-up costs, advertising, etcīased on similar bikes, you can expect sales to follow this 'Demand Curve':.

Now you want to make lots of them and sell them for profit. You have designed a new style of sports bicycle! So the ball reaches the highest point of 12.8 meters after 1.4 seconds. Then find the height using that value (1.4) The method is explained in Graphing Quadratic Equations, and has two steps:įind where (along the horizontal axis) the top occurs using −b/2a: Note: You can find exactly where the top point is! The factors of −15 are: −15, −5, −3, −1, 1, 3, 5, 15īy trying a few combinations we find that −15 and 1 work Multiply to give a×c, and add to give b' method in Factoring Quadratics: There are many ways to solve it, here we will factor it using the 'Find two numbers that 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: