IM Alg1.7.8 Practice: Rewriting Quadratic Expressions in Factored Form (Part 3)

Author:GeoGebra Classroom Activities, IM Algebra 1, Geometry, Algebra 2

Match each quadratic expression given in factored form with an equivalent expression in standard form. One expression in standard form has no match.

Both and contain a sum and a difference and have only 3 and in each factor. If each expression is rewritten in standard form, will the two expressions be the same? Explain or show your reasoning.

Show that the expressions and are equivalent.

The expressions and are equivalent and can help us find the product of two numbers. Which two numbers are they?

Write as a product of a sum and a difference, and then as a difference of two squares. What is the value of ?

Write each expression in factored form. If not possible, write “not possible.”

What are the solutions to the equation ?

Select all that apply

A
and
B
and
C
and
D
and

Check my answer (3)

Create a diagram to show that (x-3)(x-7) is equivalent to x²-10x+21.

Mai fills a tall cup with hot cocoa, 12 centimeters in height. She waits 5 minutes for it to cool. Then, she starts drinking in sips, at an average rate of 2 centimeters of height every 2 minutes, until the cup is empty. The function

gives the height of hot cocoa in Mai’s cup, in centimeters, as a function of time, in minutes. Sketch a possible graph of

in the applet below. Be sure to include a label and a scale for each axis.

What quantities do the domain and range represent in this situation?

Describe the domain and range of .

One bacteria population, , is modeled by the equation , where is the number of days since it was first measured. A second bacteria population, , is modeled by the equation , where is the number of days since it was first measured. Which statement is true about the two populations?

Select all that apply

A
The second population will always be larger than the first.
B
Both populations are increasing.
C
The second bacteria population decreases more rapidly than the first.
D
When initially measured, the first population is larger than the second.

Check my answer (3)

IM Alg1.7.8 Practice: Rewriting Quadratic Expressions in Factored Form (Part 3)

Match each quadratic expression given in factored form with an equivalent expression in standard form. One expression in standard form has no match.

Write each expression in factored form. If not possible, write “not possible.”

Create a diagram to show that (x-3)(x-7) is equivalent to x²-10x+21.

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