Graphing+Quadratic+Functions-Target+E-Using+a+Quad-Guided+Learning

Target E: Use key features of a quadratic function’s graph to answer a contextual problem.
https://i.ytimg.com/vi/zLmxgcAz10I/hqdefault.jpg Adapted from work by Rachel Fruin ||
 * [[image:Discuss this.png width="208" height="116"]] || Dave thinks that Michael Jordan could hang in the air for at least two seconds during his famous free throw line dunk. Wally disagrees with Dave. Whom do you agree with and why?

In this target, we will be using a graphing calculator to graph a quadratic function and find key features of the graph. Before moving on to contextual problems, let's familiarize ourselves with how to graph a quadratic function using a graphing calculator, and find pieces of information such as the x-intercepts and the vertex.

In order to find the x-intercepts (solutions/roots/zeroes) of a quadratic function using a graphing calculator, follow these steps: 1) Enter the function into "Y=" 2) Press "GRAPH" and adjust the window by pressing "WINDOW" until you can see the graph (make sure you can see where the parabola intersects with the x-axis). 3) Press "2nd" and "TRACE" and select "ZERO". A blinking cursor should appear on the screen. *Important: once the cursor appears only use the right and left arrow keys to move the cursor. Do NOT use the up and down arrow keys. 4) Set the Left Bound: Move the cursor to one of the x-intercepts. Then continue to move the cursor to the left by pressing the left arrow key 3 times. Press "ENTER" 5) Set the Right Bound: Move the cursor back to the same x-intercept. Then continue to move the cursor to the right by pressing the right arrow key 3 times. Press "ENTER" 6) Press "ENTER" one more time in order for the calculator to find the x-intercept.
 * Using a Graphing Calculator to Find X-Intercepts**

Repeat this process to find the other x-intercept (if needed).

In order to find the vertex of a quadratic function using a graphing calculator, follow these steps: 1) Enter the function into "Y=" 2) Press "GRAPH" and adjust the window by pressing "WINDOW" until you can see the graph (make sure you can see the vertex of the parabola). 3) Press "2nd" and "TRACE" and select "MINIMUM" or "MAXIMUM". This will depend on the individual problem. A blinking cursor should appear on the screen. *Important: once the cursor appears only use the right and left arrow keys to move the cursor. Do NOT use the up and down arrow keys. 4) Set the Left Bound: Move the cursor to the vertex. Then continue to move the cursor to the left by pressing the left arrow key 3 times. Press "ENTER". 5) Set the Right Bound: Move the cursor back to the vertex. Then continue to move the cursor to the right by pressing the right arrow key 3 times. Press "ENTER". 6) Press "ENTER" one more time in order for the calculator to find the location oft the vertex.
 * Using a Graphing Calculator to Find the Maximum/Minimum of a Vertex**

Watch the videos below to see how to use a graphing calculator to find the x-intercepts and vertex of the quadratic function f(x) = x 2 - 5x - 6.

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When we are looking at quadratic functions in relation to context, we use a special quadratic equation in order to represent the motion (height in feet with respect to time) that takes place. This is the vertical motion equation: //h(t) = -16t// 2 //+ v 0 t + h 0 // where //v 0 // represents the initial (starting) velocity or speed of a given object and //h 0 // represents the initial (starting) height of an object before any motion has taken place. Let's take a look at how we can use this equation to solve a contextual problem.
 * Using a Graphing Calculator to Solve Vertical Motion Context Problems**

A 6 foot tall quarterback is practicing his throws. On average, he starts off throwing the football at a speed of 75 feet per second. How long is the ball typically in the air? What is the maximum height that the football reaches? Assume he releases the ball at a height of 6 feet.
 * Example:**

Before we can use the graphing calculator to help answer the questions from the example problem, we first need to come up with the equation to represent this situation. This is where the vertical motion equation comes into play. We need to write the equation by substituting in the initial velocity of the football (75 feet per second) for //v 0 ,// and the starting height of the football (6 feet) in for //h 0 //. So the equation that can be used to represent the path of the football when the player releases the ball is: h(t) = -16t 2 + 75t + 6. Now that we have our function, watch the video below to see how to use the graphing calculator to answer the questions from the example problem.

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A swimmer decides to dabble in some minor league diving. She decides to give it her best and dive off the high diving board, which is 10 feet above the surface of the water. Before jumping, she bounced on the diving board a few times to give herself a starting speed of 30 feet per second.
 * Graphing Quadratic Functions-Target E-Using a Quad-Quick Check**

1) After how many seconds does the diver reach her maximum height? 2) How long does it take for the diver to reach the surface of the water?

Round your answers to the nearest hundredth.

Graphing Quadratic Functions-Target E-Using a Quad-Quick Check Solutions