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Solve Quadratic Equations

By Graphing

Today you will need:

  1. Notes
  2. Pencil
  3. Positive Attitude :-)

Grab a warm-up off the wooden desk and get started!

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Goals:

  • Solve Quadratic equations by graphing

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Warm-up #1

Simplify. Give exact answers.

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Warm-up #2

Find each product.

Simplify. Answer should be exact.

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Forms of Quadratic Functions

x-intercepts

y-intercept

vertex

open up/down

Key characteristics:

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Forms of Quadratic Functions

Standard Form

Vertex Form

Factored Form

Match the following quadratic functions to their graphs. What strategies did you use?

A.

B.

C.

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Solving Quadratics by graphing

To solve a quadratic by graphing the function must be in standard form set equal to zero. There can be at most 2 solutions to any quadratic function.

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Log on to desmos!

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Log on to desmos!

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Finding the vertex is helpful!

How to find the vertex from…

Standard Form

Vertex Form

Factored Form

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Solve by Graphing

  1. Find the vertex
  2. Make a table
  3. Plot the points
  4. Find the zeros!

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Solve by Graphing

x

y

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Solve by Graphing

  • Find the vertex
  • Make a table
  • Plot the points
  • Find the zeros!

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Solve by Graphing

  • Find the vertex
  • Make a table
  • Plot the points
  • Find the zeros!

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Reflection Questions

  1. How can you use a graph to solve a quadratic equation in one variable?

  • After you find a solution graphically, how can you check your result algebraically?

  • How can you determine graphically that a quadratic equation has no solution?

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Solve by Graphing

x

y

  • Find the vertex
  • Make a table
  • Plot the points
  • Find the zeros!

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Solve by Graphing

x

y

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Today’s google form!

Don’t forget to complete the google form to receive your participation/attendance credit for today. :-)

https://forms.gle/hqET1CbuuuppFi2m7

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What do you

see

notice

wonder?

How do we solve functions (or system of functions) graphically?

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Toss the Squish!

Today I learned... relating to exponential functions.

One question I still have is...

I know that I need to work more on...

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Independent Practice: Delta Math

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Resources

  • Notes

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Mod 7 Standards

http://education.ohio.gov/getattachment/Topics/Learning-in-Ohio/Mathematics/Ohio-s-Learning-Standards-in-Mathematics/ALGEBRA-1-Standards.pdf.aspx?lang=en-US

�Critical Area of Focus #3: Descriptive Statistics

In middle school, students developed an understanding of statistical problem solving through the format of the GAISE Model. They were expected to display numerical data and summarize it using measures of center and variability. By the end of middle school, students were creating scatter plots and recognizing linear trends in data. Now, they apply those concepts by using the GAISE model in the context of real-world applications. Students develop formal means of assessing how a model fits data. They use regression techniques to describe approximately linear relationships between quantities. Students use graphical representations and knowledge of the context to make judgements about the appropriateness of linear models. In Algebra 2. Mathematics 3, students will look at residuals to analyze the goodness of fit.

Statistics and Probability Overview

Interpreting Categorical and Quantitative Data

  1. Summarize, represent, and interpret data on a single count or measurement variable.
  2. Summarize, represent, and interpret data on two categorical and quantitative variables.
  3. Interpret linear models.

The GAISE Model (ODE Model Curriculum)

Guidelines for Assessment and Instruction in Statistics Education Report

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Mod 8 Standards

http://education.ohio.gov/getattachment/Topics/Learning-in-Ohio/Mathematics/Ohio-s-Learning-Standards-in-Mathematics/ALGEBRA-1-Standards.pdf.aspx?lang=en-US

�S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots) in the context of real-world applications using the GAISE model.

S.ID.2 In the context of real-world applications by using the GAISE model, use statistics appropriate to the shape of the data distribution to compare center (median and mean) and spread (mean absolute deviation, interquartile range, and standard deviation) of two or more different data sets.

S.ID.3 In the context of real-world applications by using the GAISE model, interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.�c. Fit a linear function for a scatterplot that suggests a linear association.

S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.

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