for the function below, find the direction of opening, the equation for the axis of symmetry, and...

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Solving Quadratics by Graphing

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By hand: Find the AOS, then plug in to find the y-value of the vertex. In the calculator: Graph the function, then press 2 nd TRACE 3 (min.) or 4 (max.)

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Page 1: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

Solving Quadratics by Graphing

Page 2: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the graph.

y = -2x2 + 8x – 3

How could we find the vertex?

Warm Up

Page 3: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

By hand: Find the AOS, then plug in to find the y-value of the vertex.

In the calculator: Graph the function, then press 2nd TRACE 3 (min.) or 4 (max.)

We can find the vertex by hand or in the calculator

Page 4: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

y = -2x2 + 8x – 3Example:

Page 5: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

y = 3x2 – 12x + 11

y = -x2 – 4x – 1

Examples:

Page 6: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

Homework Solutions

Page 7: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

Work with your partners to complete the investigation at the top of your notes.

Investigation

Page 8: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

When a>1, the graph stretches (gets narrower)

When 0<a<1, the graph compresses (gets wider)

Summarize

Page 9: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

Complete p. 257 (1-4) in your workbook

Apply your knowledge

Page 10: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

1.C2.G3.D4.F

Solutions:

Page 11: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

What does it mean to solve the equation 4x – 1 = 7? How would you solve it?

How might we solve the equation

x2 – 2x = 15?

SOLVING QUADRATICS

Page 12: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

Our goal is to find the x-values that make an equation true. This was simple for linear equations, but quadratics require a little more effort.

Solving quadratics

Page 13: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

GraphingFactoring (yay!)Completing the squareQuadratic formula

We will spend about a day on each of these!

Four ways to solve quadratics:

Page 14: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

How are the following terms related?SolutionRootZerox-intercept

How many do we expect for quadratics?

Solving by graphing

Page 15: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

What is another word for x-intercept?

What are the x-intercepts of the quadratic function graphed below?

Page 16: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

What are the roots of this function?

Page 17: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

Sometimes it is difficult to determine the exact solutions to a quadratic equation. Fortunately, our calculators can help.

What are the zeros of this quadratic?

Page 18: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

To find the solutions/roots/x-intercepts/zeros:Step 1: Set Equation = 0 Step 2: Let Y1 = 0 Step 3: Let Y2 be the quadratic portion of

the equation.Step 4: Press GraphStep 5: Press Trace to one of the x –

interceptsStep 6: Press 2nd calc, 5, Enter, Enter, Enter.Step 7: Repeat 5 – 6 for other intercept

Solving by graphing

Page 19: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

x2 – 2x = 15

x2 + 12 = 0

Examples:

14133 2 xx

Page 20: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

7x2 + 4x – 9 = 0

z2 + 7z = -10

x2 = 10x – 24

You try!

Page 21: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

Practice

Page 22: For the function below, find the direction of opening, the equation for the axis of symmetry, and the y-intercept. Use this information to sketch the

Quiz

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Algebra 2 Honors: Quadratic Functions 12-3: Example: For the quadratic function , identify the vertex, the y-intercept, x-intercept(s), and the axis of symmetry. Graph the function

Graph each function. Find the y-intercept and state the ... · PDF fileGraph each function. Find the y-intercept and state the ... data shown below displays exponential ... y-intercept

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Crystallographic Symmetry€¦ · Types of Symmetry • Rotational symmetry about a line • Rotary-inversion symmetry about a line • Translational symmetry • Screw symmetry •

Today’s Objectives:. Warm Up a)Find the y-intercept, the axis of symmetry, and the vertex b)Make a table c)Graph the function d)State whether the function

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Graphing Parabolas Using the Vertex Axis of Symmetry & y-Intercept By: Jeffrey Bivin Lake Zurich High School [email protected] Last Updated: October

INDEX Symmetry Picture1 Symmetry in the field of mathematics Picture2 Reflection symmetry Symmetry in history, religion, and culture picture3 Symmetry

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The Sequential Intercept Model - Policy Research · PDF fileHistory and Impact of the Sequential Intercept Model. The Sequential Intercept Model (SIM) was developed over several years

Research on Mechanics Symmetry Ontology · movement process symmetry, the symmetry of space movement, cposs-state process symmetry, the symmetry of transformation of materiel, energy

Warm- UpFebruary 26 1. What is the vertex, axis of symmetry, max./min, y-intercept, and direction of opening of the following y = -2x 2 – 8x – 3. 2. Find

4.2 Quadratic Functions – Vertex and Intercept Form...2+ + 1. Opens up if >0,Opens down if

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