Introduction to Quadratics

Introduction to Quadratic Functions

Ph-USA Guru

Students will:

• Graph quadratic functions.

• Find and interpret the maximum and minimum values of a quadratic function.

Multiple Choice

Find the domain and range of the relation

{(–4, 1), (0, 0), (1, –4), (2, 0), (–2, 0)}. Determine whether the relation is a function.

• D = {–4, –2, 0, 1, 2},

  R = {–4, 0,1}; yes

• D = {0, 1, 2}, R = {0, 1}; yes

• D = {–4, 0, 1},

  R = {–4, –2, 0, 1, 2}; no

• D = {–2, –4}; R = {–4, 0, 1}; yes

Multiple Choice

Find the value of f(4) for f(x) = 8 – x – x².

• 28

• 12

• -12

• -16

Multiple Choice

f(x) = x² + 5, find f(2)

• 7

• -1

• 9

• -9

Multiple Choice

In a fully simplified quadratic equation, the highest degree is:

• 1

• 2

• 3

• 4

Multiple Choice

What is the best word to describe the shape of this graph?

• Curve

• U-Shape

• Parabola

• UpSide-Down Umbrella

Multiple Choice

What kind of function does the graph represent?

• Linear

• Quadratic

• Other Function

• Not a Function

Multiple Choice

What is the difference between the degree of linear and quadratic functions?

• Linear: 1, Quadratic: 2

• Linear: 2, Quadratic: 1

• Linear: 0, Quadratic: 1

• Linear: 1, Quadratic: 0

Poll

Any questions?

Open Ended

If you said YES (you have question), please write it down.

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The video will help with clarifying the lead coefficient and degree of the polynomial.

Take notes from it to help remember the key points.​

Leading coefficient and degree of a polynomial

​Notes:
Add to your notebook

Show that g represents a quadratic function. Identify a, b, and c.

​In your notebook simplify g(x): Use the distribution property.

Show that g represents a quadratic function. Identify a, b, and c.

​​In your notebook simplify g(x): Use the distribution property.

Poll

Any questions?

Show that g represents a quadratic function. Identify a, b, and c.

​​In your notebook simplify g(x): Use the distribution property.

Open Ended

Let me know if you need more examples.

What is a quadratic function?

Parts of a Parabola

Vertex and Axis of symmetry

• VERTEX: lowest point or a highest point

• AXIS OF SYMMETRY:  a line about which the parabola is symmetrical (balanced)

Quick Review

Maximum: top of curve ---- Minimum: bottom of curve

Be sure to have your notes ready for when I see you on Wednesday.

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A good quick overview of quadratic equations.