课程： 5.17 使用图形赤道等量的图形计算计算器

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选择节使用图形二次方平的图形计算计算器

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使用图形二次方平的图形计算计算器
An arrow is shot straight up into the air from 5 feet above the ground with a velocity of 18 ft/s. The quadratic expression that represents this situation is $\begin{align*}5 + 18t - 16t^2\end{align*}$ , where t is the time in seconds. At what time does the arrow reach its maximum height and what is that height?
::箭头从地面上5英尺直直射到空中,速度为18英尺/秒。表示这种情况的二次形表达式是 5+18t-16t2,其时间是几秒。箭头何时达到最大高度,高度是多少?

Graphing Quadratic Equations
::刻度等量图形

A graphing calculator can be a very helpful tool when graphing parabolas. This concept outlines how to use the TI-83/84 to graph and find certain points on a parabola .
::图形计算器在绘制parabolas图时可以是一个非常有用的工具。这个概念概述了如何使用 TI-83/84 来绘制图解和找到抛物线上的某些点。

Let's graph $\begin{align*}y=-3x^2+14x-8\end{align*}$ using a graphing calculator.
::让我们使用图形计算器来绘制 y3x2+14x-8 。

Using a TI-83/84, press the $\begin{align*}Y=\end{align*}$ button. Enter in the equation . Be careful not to confuse the negative sign and the subtraction sign. The equation should look like $\begin{align*}y=-3x\text{^}2+14x-8\end{align*}$ or $\begin{align*}y=-3x^2+14x-8\end{align*}$ . Press GRAPH.
::使用 TI- 83/84, 按 Y = 按钮。请在方程式中输入。注意不要混淆负符号和减号。方程式应该像 y 3x2+14x-8 或 y 3x2+14x-8 。请按 GRAPH 键。

If your graph does not look like this one, there may be an issue with your window. Press ZOOM and then 6:ZStandard, ENTER. This should give you the standard window.
::如果您的图表看起来不像这个, 您的窗口可能会有问题。按 ZOOM 键, 然后是 6: ZStandard, ENTER 。这应该给您标准窗口。

Using a graphing calculator, let's now find the vertex of the parabola above .
::使用图形计算计算器,让我们现在找到上面的抛物线的顶点。

To find the vertex, press $\begin{align*}2^{nd}\end{align*}$ TRACE (CALC). The Calculate menu will appear. In this case, the vertex is a maximum, so select 4:maximum, ENTER. The screen will return to your graph. Now, you need to tell the calculator the Left Bound. Using the arrows, arrow over to the left side of the vertex, press ENTER. Repeat this for the Right Bound. The calculator then takes a guess, press ENTER again. It should give you that the maximum is $\begin{align*}X=2.3333333\end{align*}$ and $\begin{align*}Y=8.3333333\end{align*}$ . As fractions, the coordinates of the vertex are $\begin{align*}\left(2\frac{1}{3}, 8\frac{1}{3}\right)\end{align*}$ . Make sure to write the coordinates of the vertex as a point.
::要找到顶点, 请按 TRACE (CALC) 。计算菜单将会出现。在此情况下, 顶点为最大值, 所以选择 4 : 最大值, ENTER 。屏幕会返回到您的图表。现在, 您需要告诉计算器左圆。使用箭头, 箭头到顶点左侧, 请按 ENTER 。重复此操作右圆。计算器会进行猜测, 然后再按 ENTER 键。它应该使您知道顶点的最大值是 X=2.333333333 和 Y= 8. 333333 。作为分数, 顶点的坐标是 213, 813 。请确定将顶点的坐标写为点。

Using a graphing calculator, let's find the $\begin{align*}x-\end{align*}$ intercepts of the parabola above .
::使用图形计算计算器,让我们找到上面的抛物线的 X - 截断点。

To find the $\begin{align*}x-\end{align*}$ intercepts, press $\begin{align*}2^{nd}\end{align*}$ TRACE (CALC). The Calculate menu will appear. Select 2:Zero, ENTER. The screen will return to your graph. Let’s focus on the left-most intercept . Now, you need to tell the calculator the Left Bound. Using the arrows, arrow over to the left side of the vertex, press ENTER. Repeat this for the Right Bound (keep the bounds close to the intercept). The calculator then takes a guess, press ENTER again. This intercept is $\begin{align*}X=.666667\end{align*}$ , or $\begin{align*}\left(\frac{2}{3}, 0\right)\end{align*}$ . Repeat this process for the second intercept. You should get (4, 0).
::要找到 x- intercuts, 请按第 2 TRACE (CALC) 。计算菜单将出现。选择 2: 零, ENTER 。屏幕将返回您的图表。让我们集中关注最左边的截取。现在, 您需要告诉计算器左圆圈。使用箭头, 箭头向左侧, 请按 ENTER 。重复此点, 右圆( 将界限保持接近截取) 。计算器然后进行猜测, 重新按 ENTER 。本次截取是 X= 666667 或 (23, 0) 。第二次截取时请重复此进程。您应该得到 ( 4, 0 ) 。

NOTE : When graphing parabolas and the vertex does not show up on the screen, you will need to zoom out. The calculator will not find the value(s) of any $\begin{align*}x-\end{align*}$ intercepts or the vertex that do not appear on screen. To zoom out, press ZOOM, 3:Zoom Out , ENTER, ENTER.
::注意 : 当图示 parabolas 和顶点没有出现在屏幕上时, 您需要缩放。计算器将不会找到任何 x- intercutes 或屏幕上未出现的顶点的值。要缩放, 请按 ZOOM, 3: 缩小, ENTER, ENTER 。

Examples
::实例

Example 1
::例1

Earlier, you were asked to find the time at which the arrow reaches its maximum height and to find that height.
::早些时候,有人要求你找到箭头到达最大高度的时间, 并找到那个高度。

Use your calculator to find the vertex of the parabolic expression $\begin{align*}5 + 18t - 16t^2\end{align*}$ .
::使用计算器查找抛物线表达式 5+18t- 16t2 的顶点。

The vertex is (0.5625, 10.0625). Therefore , the maximum height is reached at 0.5625 seconds and that maximum height is 10.0625 feet.
::顶部为(0.5625, 10.0625),因此,最高高度为0.5625秒,最高高度为10.0625英尺。

Example 2
::例2

Graph $\begin{align*}y=6x^2+11x-35\end{align*}$ using a graphing calculator. Find the vertex and $\begin{align*}x-\end{align*}$ intercepts. Round your answers to the nearest hundredth.
::图 y= 6x2+11x-35 使用图形化计算器。查找顶点和 x- interviews。将您的答复转至最近的第100次。

Using the steps above, the vertex is (-0.917, -40.04) and is $\begin{align*}a\end{align*}$ minimum . The $\begin{align*}x-\end{align*}$ intercepts are (1.67, 0) and (-3.5, 0).
::使用上述步骤,顶部为(-0.917,-40.04)和最小值。 X- 截取为(1.67,0)和(- 3.5,0)。

Review
::回顾

Graph the quadratic equations using a graphing calculator. Find the vertex and $\begin{align*}x-\end{align*}$ intercepts, if there are any. If there are no $\begin{align*}x-\end{align*}$ intercepts, use algebra to find the imaginary solutions. Round all real answers to the nearest hundredth.
::使用图形化计算器来构造二次方程。如果有的话, 找到顶点和 x- intercuts。如果没有 x- intercuts, 则使用代数来寻找假想的解决方案。将所有真实答案四舍五入到最近的一百个答案。

$\begin{align*}y=x^2-x-6\end{align*}$
::y=x2-x-6 y=x2-x-6

$\begin{align*}y=-x^2+3x+28\end{align*}$
::yx2+3x+28

$\begin{align*}y=2x^2+11x-40\end{align*}$
::y=2x2+11x-40

$\begin{align*}y=x^2-6x+7\end{align*}$
::y=x2 - 6x+7 y=x2 - 6x+7

$\begin{align*}y=x^2+8x+13\end{align*}$
::y=x2+8x+13 y=x2+8x+13

$\begin{align*}y=x^2+6x+34\end{align*}$
::y=x2+6x+34

$\begin{align*}y=10x^2-13x-3\end{align*}$
::y= 10x2- 13x- 3

$\begin{align*}y=-4x^2+12x-3\end{align*}$
::y4x2+12x-3

$\begin{align*}y=\frac{1}{3}(x-4)^2+12\end{align*}$
::y=13(x- 4) 2+12

$\begin{align*}y=-2(x+1)^2-9\end{align*}$
::y&2 (x+1) 2- 9

Calculator Investigation The parent graph of a quadratic equation is $\begin{align*}y=x^2\end{align*}$ .
::二次方程的母图是 Y=x2 。

Graph $\begin{align*}y=x^2, y=3x^2\end{align*}$ , and $\begin{align*}y=\frac{1}{2}x^2\end{align*}$ on the same set of axes in the calculator. Describe how $\begin{align*}a\end{align*}$ effects the shape of the parabola.
::图y=x2,y=3x2,y=12x2 和y=12x2 在计算器中的同一组轴上。描述抛物线的形状是如何作用的。

Graph $\begin{align*}y=x^2, y=-x^2\end{align*}$ , and $\begin{align*}y=-2x^2\end{align*}$ on the same set of axes in the calculator. Describe how $\begin{align*}a\end{align*}$ effects the shape of the parabola.
::图 y=x2,yx2, 和 y2x2 在计算器中的同一组轴上。描述一个形状如何影响抛物线的形状。

Graph $\begin{align*}y=x^2, y=(x-1)^2\end{align*}$ , and $\begin{align*}y=(x+4)^2\end{align*}$ on the same set of axes in the calculator. Describe how $\begin{align*}h\end{align*}$ effects the location of the parabola.
::图y=x2,y=(x-1)2,y=(x+4)2 和y=(x+4)2 在计算器中同一组轴上。请描述参数位置的 h 效果。

Graph $\begin{align*}y=x^2, y=x^2+2\end{align*}$ , and $\begin{align*}y=x^2-5\end{align*}$ on the same set of axes in the calculator. Describe how $\begin{align*}k\end{align*}$ effects the location of the parabola.
::图y=x2,y=x2+2,y=x2+5在计算器中的同一组轴上。描述 k 如何影响抛物线的位置。

Real World Application The path of a baseball hit by a bat follows a parabola. A batter hits a home run into the stands that can be modeled by the equation $\begin{align*}y=-0.003x^2+1.3x+4\end{align*}$ , where $\begin{align*}x\end{align*}$ is the horizontal distance and $\begin{align*}y\end{align*}$ is the height (in feet) of the ball. Find the maximum height of the ball and its total distance travelled.
::被球棒击打的棒球路径与抛物线相继。击击击击打一个以 y = 0.003x2+1.3x+4 等式模拟的站台, 其中 x 是水平距离, y 是球的高度。找到球的最大高度及其所穿行的总距离。

Review (Answers)
::回顾(答复)

Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键。

章节大纲

常规

使用图形二次方平的图形计算计算器

Graphing Quadratic Equations ::刻度等量图形

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Review ::回顾

Review (Answers) ::回顾(答复)

Graphing Quadratic Equations
::刻度等量图形

Examples
::实例

Example 1
::例1

Example 2
::例2

Review
::回顾

Review (Answers)
::回顾(答复)