Solving Quadratic Eqns w Zero Product Property: IM Alg1.7.4
[url=https://im.kendallhunt.com/HS/teachers/1/7/4/preparation.html]“Solving Quadratic Equations with the Zero Product Property”[/url] from IM Algebra I © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg1.7.4 Lesson
- IM Alg1.7.4 Lesson: Solving Quadratic Equations with the Zero Product Property
- Alg1.7.4 Practice
- IM Alg1.7.4 Practice: Solving Quadratic Equations with the Zero Product Property
IM Alg1.7.4 Lesson: Solving Quadratic Equations with the Zero Product Property
What values of the variables make each equation true?
[math]6+2a=0[/math]
[math]7b=0[/math]
[math]7\left(c-5\right)=0[/math]
[math]g\cdot h=0[/math]
For each equation, find its solution or solutions. Be prepared to explain your reasoning.
[math]x-3=0[/math]
[math]x+11=0[/math]
[math]2x+11=0[/math]
[math]x\left(2x+11\right)=0[/math]
[math]\left(x-3\right)\left(x+11\right)=0[/math]
[math]\left(x-3\right)\left(2x+11\right)=0[/math]
[math]x\left(x+3\right)\left(3x-4\right)=0[/math]
Use factors of 48 to find as many solutions as you can to the equation [math]\left(x-3\right)\left(x+5\right)=48[/math]
Once you think you have all the solutions, explain why these must be the only solutions.
[size=150]We have seen quadratic functions modeling the height of a projectile as a function of time.[br][br]Here are two ways to define the same function that approximates the height of a projectile in meters, [math]t[/math] seconds after launch:[/size][br][math]h\left(t\right)=-5t^2+27t+18[/math] [math]h\left(t\right)=\left(-5t-3\right)\left(t-6\right)[/math][br][br]Which way of defining the function allows us to use the zero product property to find out when the height of the object is 0 meters?
Without graphing, determine at what time the height of the object is 0 meters. Show your reasoning.[br]
IM Alg1.7.4 Practice: Solving Quadratic Equations with the Zero Product Property
[size=150]If the equation [math]\left(x+10\right)x=0[/math] is true, which statement is also true according to the zero product property?[/size]
[size=150]What are the solutions to the equation [math]\left(10-x\right)\left(3x-9\right)=0[/math]?[/size]
Solve each equation.
[math]\left(x-6\right)\left(x+5\right)=0[/math]
[math]\left(x-3\right)\left(\frac{2}{3}x-6\right)=0[/math]
[math]\left(-3x-15\right)\left(x+7\right)=0[/math]
[size=150]Consider the expressions [math]\left(x-4\right)\left(3x-6\right)[/math] and [math]3x^2-18x+24[/math].[/size][br][size=150][br]Show that the two expressions define the same function.[/size]
[size=150]Kiran saw that if the equation [math]\left(x+2\right)\left(x-4\right)=0[/math] is true, then, by the zero product property, either [math]x+2[/math] is 0 or [math]x-4[/math] is 0. He then reasoned that, if [math]\left(x+2\right)\left(x-4\right)=72[/math] is true, then either [math]x+2[/math] is equal to 72 or [math]x-6[/math] is equal to 72. [/size][br][br]Explain why Kiran’s conclusion is incorrect.
[size=150]Andre wants to solve the equation [math]5x^2-4x-18=20[/math]. He uses a graphing calculator to graph [math]y=5x^2-4x-18[/math] and [math]y=20[/math] and finds that the graphs cross at the points [math]\left(-2.39,20\right)[/math] and [math]\left(3.19,20\right)[/math].[br][/size][br]Substitute each [math]x[/math]-value Andre found into the expression [math]5x^2-4x-18[/math]. Then evaluate the expression.[br]
Why did neither solution make [math]5x^2-4x-18[/math] equal exactly 20?[br]
[size=150]Select [b]all[/b] the solutions to the equation [math]7x^2=343[/math].[/size]
[size=150]Here are two graphs that correspond to two patients, A and B. Each graph shows the amount of insulin, in micrograms (mcg) in a patient' body [math]h[/math] hours after receiving an injection. The amount of insulin in each patient decreases exponentially.[br][/size][br][img]data:image/png;base64,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[/img][br]Select [b]all[/b] statements that are true about the insulin level of the two patients.
[size=150]Han says this pattern of dots can be represented by a quadratic relationship because the dots are arranged in a rectangle in each step.[/size][br][img]data:image/png;base64,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[/img][br][br]Do you agree? Explain your reasoning.