Question
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Consider the Quadratic function .
Its vertex is
Its largest -intercept is .
Its -intercept is

Ask by Guzman Chang. in the United States
Mar 16,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The vertex is , the largest -intercept is , and the -intercept is .

Solution

We start with the quadratic function
1. Finding the vertex
The vertex of a quadratic function is given by
Here, and , so
Next, we find by evaluating :
Calculate :
Now, compute the rest:
Thus,
So, the vertex is
2. Finding the -intercepts
To find the -intercepts, set :
This quadratic factors as
Setting each factor equal to zero gives:
which implies
The largest -intercept is
3. Finding the -intercept
The -intercept is found by evaluating :
Thus, the -intercept is
Summary
  • The vertex is .
  • The largest -intercept is .
  • The -intercept is .

Answered by UpStudy AI and reviewed by a Professional Tutor

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The Deep Dive

The vertex of the quadratic function can be found using the vertex formula . Here, and , giving us . To find the corresponding -coordinate, substitute back into the function. The vertex is at .
Next, to find the largest -intercept, we can use the quadratic formula given by . Plugging in values here gives us two -intercepts: and . The largest is .
Lastly, to find the -intercept, we evaluate the function at : . So the -intercept is .
In summary:
  • Vertex:
  • Largest -intercept:
  • -intercept:

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