Quadratic FunctionsLearning Goals & Scales

Identify the Quadratic Functions1 2

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I can identify quadratic functions from a graph.1. I cannot correctly identify a quadratic

function from a graph.2. I can sometimes identify a quadratic

function from a graph.3. I can usually identify a quadratic function

from a graph.4. I can easily identify a quadratic function

from a graph and explain how to distinguish it from other functions.

Identify the Quadratic Functions y = 2x² + 3x – 7 f(x) = x² y = 4x + 3 y =|x + 3|-4 f(x) = -x² - 9 y = (x – 5)² + 2 y = 12

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X

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X

I can identify quadratic functions from an equation.1. I cannot correctly identify a quadratic

function from an equation.2. I can sometimes identify a quadratic

function from an equation.3. I can usually identify a quadratic function

from an equation.4. I can easily identify a quadratic function

from an equation and explain how to discern that.

Identify key features of a ParabolaIdentify:The VertexThe MinimumThe Y-InterceptThe Solution/sThe Axis of SymmetryThe DomainThe RangeConcavity (Open Up / Down)

I can identify key features of graphs.1. I cannot identify any parts of a parabola.2. I can sometimes identify some, but not all

parts of a parabola.3. I can identify most of the parts of a

parabola.4. I can easily identify all of the parts of a

parabola, and can explain their interrelatedness.

Spot the Form y = (x – 3)² + 2

y = (x – 6)(x + 5)y = 4x² + 2x - 9

y = -2(x – 1)² + 2f(x) = 3x² - 6

Vertex Form

Vertex Form

Vertex Form & Standard Form

Standard Form

Factored Form

I can identify whether a quadratic function is in standard, vertex, or factored form.

1. I cannot tell what form a quadratic equation is in.

2. I can identify some forms of quadratic equations.

3. I understand how to tell the difference and can usually identify each form.

4. I can easily identify which form an equation is in, and explain how I know.

Convert the quadratic from vertex to standard form.

f(x) = 2(x-5)² -4

1. FOIL the argument

4. Combine Like Terms

3. Multiply by “a”

2. Combine Like Terms

I can convert a quadratic from vertex to standard form.1. I cannot convert a quadratic from vertex to standard

form.2. I understand the procedure, but I cannot execute it.3. I understand the procedure, and can execute it.4. I understand the procedure, can execute it, and

understand why I might want to do it.

Convert the quadratic from factored to standard form.

f(x) = (x-5)(x + 6)

1. FOIL the argument

2. Combine Like Terms

I can convert a quadratic from factored to standard form.1. I cannot convert a quadratic from factored to standard

form.2. I understand the procedure, but I cannot execute it.3. I understand the procedure, and can execute it.4. I understand the procedure, can execute it, and

understand why I might want to do it.

Convert the quadratic from standard to vertex form.

f(x) = x² - 4x - 5

1. A = a

2. h = -b/2a

3. k = f(-b/2a )

I can convert a quadratic from standard to vertex form.1. I cannot convert a quadratic from standard to vertex

form.2. I understand the procedure, but I cannot execute it.3. I understand the procedure, and can execute it.4. I understand the procedure, can execute it, and

understand why I might want to do it.

Convert the quadratic from standard to factored form.

f(x) = x² - 4x - 5

1. (x – p)(x – q)

2. P and q are factors of AC that add up to B

I can convert a quadratic from standard to factored form.1. I cannot convert a quadratic from standard to factored

form.2. I understand the procedure, but I cannot execute it.3. I understand the procedure, and can execute it.4. I understand the procedure, can execute it, and

understand why I might want to do it.

Find key features from equationsFind: Where Found:The VertexThe MinimumThe Y-InterceptThe Solution/sThe Axis of SymmetryThe DomainThe RangeConcavity (Open Up / Down)

Vertex Form (h,k) (or Standard Form)

Vertex Form @ k (or Standard Form)

Standard Form @ (0, C)

Factored Form @ p and q

Vertex Form @ x = h (or Standard Form)

Any Form @ (-∞, +∞)

Vertex Form @ (-∞, k] or [k, +∞)

Any Form up if a is positive, else down

Write a quadratic function given zeros.

Given zeros of 4 and -5Write a quadratic function in standard form

with those zeros.

1. f(x) = a (x – p)(x – q)

2. FOIL together

I can write quadratic equations with given zeros.1. I cannot write a quadratic from given zeros.2. I understand the procedure, but I cannot execute it.3. I understand the procedure, and can execute it.4. I understand the procedure, can execute it, and

understand why I might want to do it.

Solve By FactoringFactor the Binomial Factor the Trinomial

y = 14x² - 7x y = x² + 5x - 6

0 = 14x² - 7x0 = 7x(2x – 1)

7x = 0 or 2x - 1 = 07 7 +1 +1x=0 or 2x = 1

2 2 x = ½ Solution: x = {0, ½ }

0 = (x + 6)(x – 1)(x + 6)= 0 or (x –

1) = 0 -6 -6 +1 +1 x = -6 x = 1

Solutions: x = {-6, 1}

H. Students will be able to solve quadratic equations by factoring using the Zero Product Property.1. I cannot solve quadratic equations by

factoring.2. I can solve some quadratic equations by

factoring with help.3. I can solve any factorable quadratic

equations by factoring with only minor errors.

4. I can easily solve factorable quadratic equations by factoring.

Solve by Completing the Squarex² + 4x -7 = y

x² + 4x -7 = 0+7 +7

x² + 4x = 7x² + 4x + __= 7 + __x² + 4x + 4 = 7 + 4x² + 4x + 4 = 11 (x+2)² = 11 x+ 2 = ± √11x = {-2+√11 , -2-√11}

H. Students will be able to solve quadratic equations by completing the square.1. I cannot solve quadratic equations by

completing the square.2. I can solve quadratic equations by

completing the square with help.3. I can solve quadratic equations by

completing the square with only minor errors.

4. I can easily solve quadratic equations by completing the square.

I. Students will be able to use the discriminant to determine the nature of the roots of a quadratic equation.

1. I am not able to use the discriminant to determine the nature of the roots of a quadratic equation.

2. I can find the discriminant, but I cannot use it to find the nature of the roots of a quadratic equation.

3. I can find the discriminant, and I can use it to find the nature of the roots of a quadratic equation.

4. I can find the discriminant, and I can use it to find the nature of the roots of a quadratic equation, and I can explain why.

J. Students will be able to identify real and imaginary parts of complex numbers and perform basic operations.

1. I cannot identify real and imaginary parts of complex numbers and perform basic operations.

2. I can identify real and imaginary parts of complex numbers, but cannot perform basic operations.

3. I can identify real and imaginary parts of complex numbers and perform basic operations with only minor errors.

4. I can easily identify real and imaginary parts of complex numbers and perform basic operations.

K. Students will be able to solve quadratic equations over the complex number system.1. I cannot solve quadratic equations over the

complex number system.2. I can solve quadratic equations over the

complex number system with help.3. I can solve quadratic equations over the

complex number system with only minor errors.

4. I can easily solve quadratic equations over the complex number system.

L. Students will be able to solve a quadratic function with the quadratic formula.1. I cannot solve a quadratic function with the

quadratic formula.2. I can solve a quadratic function with the

quadratic formula with help.3. I can solve a quadratic function with the

quadratic formula with only minor errors.4. I can easily solve a quadratic function with

the quadratic formula.