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Title: Polynomial functions

Grade: 1400-a Lesson: S2-L2

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Consider the quadratic function \$f(x) = x^2 + 4x + 4\$. Let’s find the roots of this function.
2	Step	Finding the solution of the quadratic function means f(x) = 0	\$ x^2 + 4x + 4 = 0\$
3	Formula:	The quadratic formula states that the roots of the quadratic equation \$ax^2 + bx + c = 0\$ can be found using the following formula:	\$ x = ( (-b) pm \sqrt(b^2 - 4ac))/(2a) \$
4	Hint	where a = 1, b = 4, and c = 4, now substitute the values in the above formula then after simplification	\$ x = ( (-4) pm \sqrt(4^2 - 4(1)(4)))/(2(1)) \$ \$ x = - 2 \$
5	Step	The roots of the function are \$ x = - 2\$.
6	Choice.A	This choice is Correct. The quadratic function can be factored as \$(x + 2)^2\$, yielding the root x = -2	x = - 2
7	Choice.B	This option is Incorrect. -3 is not a root of the given quadratic function	x = - 3
8	Choice.C	Incorrect. This option is not a root of the given quadratic function	x = - 4
9	Choice.D	This option is incorrect because it doesn’t correspond to any root of the given quadratic function	x = - 5
10	Answer	Option	A
11	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Consider the quadratic function \$f(x) = x^2 + 4x + 4\$.
Let’s find the roots of this function.

Step

Finding the solution of the quadratic function means f(x) = 0

\$ x^2 + 4x + 4 = 0\$

Formula:

The quadratic formula states that the roots of the quadratic equation \$ax^2 + bx + c = 0\$ can be found using the following formula:

\$ x = ( (-b) pm \sqrt(b^2 - 4ac))/(2a) \$

Hint

where a = 1, b = 4, and c = 4, now substitute the values in the above formula then after simplification

\$ x = ( (-4) pm \sqrt(4^2 - 4(1)(4)))/(2(1)) \$

\$ x = - 2 \$

Step

The roots of the function are \$ x = - 2\$.

Choice.A

This choice is Correct. The quadratic function can be factored as \$(x + 2)^2\$, yielding the root x = -2

x = - 2

Choice.B

This option is Incorrect. -3 is not a root of the given quadratic function

x = - 3

Choice.C

Incorrect. This option is not a root of the given quadratic function

x = - 4

Choice.D

This option is incorrect because it doesn’t correspond to any root of the given quadratic function

x = - 5

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?