Algebra 1 | Unit 7 | Lesson 9: Solving Quadratic Equations by Using Factored Form | Practice Problems

Find all the solutions to each equation. x(x-1)=0 (5-x)(5+x)=0 (2x+1)(x+8)=0 (3x-3)(3x-3)=0 (7-x)(x+4)=0

• x=0 and x=1

• x=±5

• x=−1/2 and x=−8

• x=1

• x=7 and x=−4

Tags

CCSS.HSA-REI.B.4B

Rewrite each equation in factored form and solve using the zero product property. d^2 -7d+6=0 x^2 +18x +81=0 u^2 +7u -60=0 x^2+0.2x+0.01=0

• d=6 and d=1

• x=−9

• u=−12 and u=5

• x=−0.1

Tags

CCSS.HSA-REI.B.4B

Here is how Elena solves the quadratic equation x^2 -3x -18 =0. Is her work correct? If you think there is an error, explain the error and correct it. Otherwise, check her solutions by substituting them into the original equation and showing that the equation remains true.

Tags

CCSS.HSA-REI.B.4B

Jada is working on solving a quadratic equation. She thinks that her solution is correct because substituting 5 for p in the original expression p^2- 5p gives 25-25 or 0. Explain the mistake that Jada made and show the correct solutions.

Tags

CCSS.HSA-REI.B.4B

Choose a statement to correctly describe the zero product property. If a and b are numbers, and a ⋅ b=0, then:

• A: Both a and b must equal 0.

• B: Neither a nor b can equal 0.

• C: Either a=0 or b=0.

• D: a+b must equal 0.

Tags

CCSS.HSA-REI.B.4B

Which expression is equivalent to x^2-7x+12?

• A: (x+3)(x+4)

• B: (x-3)(x-4)

• C: (x+2)(x+6)

• D: (x-2)(x-6)

These quadratic expressions are given in standard form. Rewrite each expression in factored form.

• (x+1)(x+6)

• (x-1)(x-6)

• (x-2)(x-3)

• (x+2)(x+3)

Select all the functions whose output values will eventually overtake the output values of function f defined by f(x)=25x^2.

• A: g(x)=5(2)^x

• B: h(x)=5^x

• C: j(x)=x^2+5

• D: k(x)=(5/2)^x

• E: m(x)=5+2^x

A piecewise function, p, is defined by this rule: p(x)=x-1, x≤−2; 2x-1, x>−2. Find the value of p at each given input.

• p(-20)=-21

• p(-2)=-3

• p(4)=7

• p(5.7)=10.4

Tags

CCSS.HSF.IF.A.2