Determine whether the function's vertex is a maximum point or a minimum point and find the coordinates of this point. Find the zeros, if any exist, and sketch the graph of the function. y=x

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.CR: Chapter Review
Problem 1E
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Determine whether the function's vertex is a maximum point or a minimum point and find the coordinates of this point. Find the zeros, if any exist, and sketch the graph of the function.
1x²
8
y = x-
Step 1
First write the function in general form, y =
Since a
y = -
1
8
-X² + x
+²
The vertex is a maximum point.
X =
The vertex is a minimum point.
0, the parabola opens downward
ax² + bx + c.
-b
2a 2.
Step 2
The coordinates of the vertex of a quadratic function of the form y = ax² + bx + c are
(=b, f(=b)
2a
2a
Use the values of a and b to determine the x-coordinate of the vertex.
-1
downward So, is the vertex a maximum or a minimum?
Transcribed Image Text:Determine whether the function's vertex is a maximum point or a minimum point and find the coordinates of this point. Find the zeros, if any exist, and sketch the graph of the function. 1x² 8 y = x- Step 1 First write the function in general form, y = Since a y = - 1 8 -X² + x +² The vertex is a maximum point. X = The vertex is a minimum point. 0, the parabola opens downward ax² + bx + c. -b 2a 2. Step 2 The coordinates of the vertex of a quadratic function of the form y = ax² + bx + c are (=b, f(=b) 2a 2a Use the values of a and b to determine the x-coordinate of the vertex. -1 downward So, is the vertex a maximum or a minimum?
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