The sides of the deck are 8, 15, and 17 feet. Since \(x\) is a side of the triangle, \(x=−8\) does not It is a quadratic equation, so get zero on one side. Since this is a right triangle we can use the Step - 4: The x-coordinates of the x-intercepts are nothing but the roots of the quadratic equation. Step - 2: Graph the quadratic expression (which is on the left side). We are looking for the lengths of the sides Here are the steps to solve quadratic equations by graphing. Find the lengths of the sides of the deck. The length of one side will be 7 feet less than the length of the other side. Justine wants to put a deck in the corner of her backyard in the shape of a right triangle, as shown below. Use the zero product property, and set each factor equal to zero: (x 2) 0 and (x + 2) 0. to help solve quadratic equations with the factoring method. First, draw the basic parabola of y x2 on the board. \(W=−5\) cannot be the width, since it's negative. Lesson 37 Activity 1: Graphing Quadratic Equations Time: 15-20 Minutes 1. Use the formula for the area of a rectangle. The area of the rectangular garden is 15 square feet. Restate the important information in a sentence. In problems involving geometric figures, a sketch can help you visualize the situation. The length of the garden is two feet more than the width. Now we use our algebra skills to solve for "x".\)Ī rectangular garden has an area of 15 square feet. 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. The y-intercept is found by plugging x 0 into the quadratic equation as y a(0)2.
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