Wright Hodges
03/22/2023 · High School
Find the zeros of the following quadratic function using the square root method. What are the \( x \)-intercepts of the graph of the function? \( f(x)=x^{2}-98 \) Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The zeros and the \( x \)-intercepts are the same. They are B. Therepts are different. The zeros are
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find the zeros of the quadratic function \( f(x) = x^2 - 98 \) using the square root method, we set the function equal to zero:
\[
x^2 - 98 = 0
\]
Next, we isolate \( x^2 \):
\[
x^2 = 98
\]
Now, we take the square root of both sides:
\[
x = \pm \sqrt{98}
\]
We can simplify \( \sqrt{98} \):
\[
\sqrt{98} = \sqrt{49 \cdot 2} = \sqrt{49} \cdot \sqrt{2} = 7\sqrt{2}
\]
Thus, the solutions for \( x \) are:
\[
x = 7\sqrt{2} \quad \text{and} \quad x = -7\sqrt{2}
\]
Therefore, the zeros of the function and the \( x \)-intercepts of the graph are:
\[
7\sqrt{2}, -7\sqrt{2}
\]
So, the correct choice is:
B. The zeros and the \( x \)-intercepts are the same. They are \( 7\sqrt{2}, -7\sqrt{2} \).
Quick Answer
B. The zeros and the \( x \)-intercepts are the same. They are \( 7\sqrt{2}, -7\sqrt{2} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit