2/9 - Factoring using Desmos

Reorder

Put the steps in order to factor: $$2x^2-2x-4$$  

• Factor out GCF:

  $$2\left(x^2-x-2\right)$$

•  Factor remaining trinomial:

  $$2\left(x-2\right)\left(x+1\right)$$

•  That's it, you're done!

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LO: SWBAT determine the factors of quadratic polynomials of the form ax²+ bx + c using Desmos

DOL: Given 5 problems, students will correctly determine the factors of quadratic polynomials of the form of ax² + bx + c, where a ≠ 1 in at least 4 of 5 questions.

ALGI.10E - Factor, if possible trinomials with real factors in the form ax2+ bx + c, including perfect square trinomials of
degree two.

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​The Same Quadratic Function

​KEYWORDS

​Equivalent
Represents

​Enter ALL answer choices in Desmos

Multiple Choice

Use Desmos to determine which equations represent the the given quadratic function?

• $$f\left(x\right)=\left(x-2\right)^2-3$$

• $$f\left(x\right)=\left(x+2\right)^2-3$$

• $$f\left(x\right)=\left(x+1\right)^2+4$$

• $$f\left(x\right)=\left(x-1\right)^2+4$$

Multiple Select

Which expressions are equivalent to
$$12x^2-48x+48$$  ?

Select TWO correct answers.

• $$12\left(x-2\right)^2$$  

• $$-12\left(x^2+4x+4\right)$$  

• $$12\left(x-4\right)\left(x-1\right)$$  

• $$-12\left(x+2\right)^2$$  

• $$12\left(x^2-4x+4\right)$$

Multiple Choice

Which of the following is equivalent to: $$x^2+7x+10$$  

• $$\left(x+2\right)\left(x+5\right)$$  

• $$\left(x-2\right)\left(x-5\right)$$  

• $$\left(x+10\right)\left(x+1\right)$$

• $$\left(x+2\right)\left(x-5\right)$$  

​Determining Single Factors

Hotspot

What two points represent the x-intercepts?

Multiple Select

Select ALL the words that mean "x-intercept".

• axis of symmetry

• vertex

• zero

• roots

• solutions

​Factors will cross on the x-intercepts

Multiple Choice

Which line represents a factor of the quadratic function?

• The blue line

• The green line

• The purple line

• The black line

Multiple Choice

Which expression is a factor of $$30x^2-4x-16$$

• $$5x+4$$

• $$3x-2$$

• $$5x-4$$

• $$3x-4$$

Multiple Choice

Which expression is a factor of $$10x^2-19x+6$$

• $$10x-3$$

• $$10x-1$$

• $$5x-3$$

• $$5x-2$$

Demonstration of Learning

DOL: Given 5
problems, students
will correctly
students will
correctly factor
expressions in the
form of ax2+ bx + c,
where a ≠1 in at
least 4 of 5
questions in at
least 4 of 5
questions.

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Open Ended

How does Desmos assist with determining factors of quadratic functions?

Use complete sentences: Desmos assist in determining factors of quadratic functions by...