SaiBook.us SAT-2

Home Course Section

Schedule Admission Social

Lesson Example Discussion Quiz: Class Homework

Step-4

Title: Polynomial functions

Grade: 1300-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^4 - 16x^2\$. Let’s find the y-intercept of this function.
2	Step	The given function	\$f(x) = x^4 - 16x^2\$
3	Step	To find the y-intercept of a function, we substitute x = 0 into the function and solve for the corresponding y-value.
4	Hint	For the quadratic function \$f(x) = x^4 - 16x^2\$, we can find the y-intercept by setting x = 0: then after simplify	\$f(0) = (0)^4 - 16(0)^2\$ \$f(0) = 0 \$
5	Step	Therefore, the y-intercept of the function \$f(x) = x^4 - 16x^2\$ is y = 0.
6	Choice.A	The y-intercept of the function occurs where x = 0. Therefore, the y-value at this point is 0, not 3, making that choice incorrect	y = 3
7	Choice.B	This option is incorrect because the y-intercept of the function occurs where x = 0, resulting in a y-coordinate of 0, rather than y = 2	y = 2
8	Choice.C	The y-intercept of the function is where x = 0, resulting in y = 0, not y = 1	y = 1
9	Choice.D	The y-intercept of the function \$ f(x) = x^4 - 16x^2 \$ is indeed at y = 0, corresponding to the point where x = 0. Therefore, this answer is correct	y = 0
10	Answer	Option	D
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^4 - 16x^2\$. Let’s find the y-intercept of this function.

Step

The given function

\$f(x) = x^4 - 16x^2\$

Step

To find the y-intercept of a function, we substitute x = 0 into the function and solve for the corresponding y-value.

Hint

For the quadratic function \$f(x) = x^4 - 16x^2\$, we can find the y-intercept by setting x = 0: then after simplify

\$f(0) = (0)^4 - 16(0)^2\$

\$f(0) = 0 \$

Step

Therefore, the y-intercept of the function \$f(x) = x^4 - 16x^2\$ is y = 0.

Choice.A

The y-intercept of the function occurs where x = 0. Therefore, the y-value at this point is 0, not 3, making that choice incorrect

y = 3

Choice.B

This option is incorrect because the y-intercept of the function occurs where x = 0, resulting in a y-coordinate of 0, rather than y = 2

y = 2

Choice.C

The y-intercept of the function is where x = 0, resulting in y = 0, not y = 1

y = 1

Choice.D

The y-intercept of the function \$ f(x) = x^4 - 16x^2 \$ is indeed at y = 0, corresponding to the point where x = 0. Therefore, this answer is correct

y = 0

Answer

Option

Sumup

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