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X -2 -1 0 1 2 y 1st differences 2nd differ ces Concave up or down? Location of vertex (______).

X -2 -1 0 1 2 y 1st differences 2nd differ ces Concave up or down? Location of vertex (______).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Lesson 14 2. *27012 X -2 -1 XTTO-2 y=x²-4 (a = 1, b = 0, c = -4) 1st differences -1 0 7 y Concave up or down? Location of vertex 3. y=x²+2x+3 (a = 1, b = 2, c = 3) 1 of 8 y 1st differences + Automatic Zoom 2nd differences 2nd differences Concave up or down? Location of vertex ( _____).
Transcribed Image Text:Lesson 14 2. *27012 X -2 -1 XTTO-2 y=x²-4 (a = 1, b = 0, c = -4) 1st differences -1 0 7 y Concave up or down? Location of vertex 3. y=x²+2x+3 (a = 1, b = 2, c = 3) 1 of 8 y 1st differences + Automatic Zoom 2nd differences 2nd differences Concave up or down? Location of vertex ( _____).
1. Use the following equations to create a table of values (sub each x value into the equation to find the y value), calculate first and second differences, state vertex and direction of concave. Check each graph on desmos. y=-x² +1 (a = -1, b = 0, c = 1) X -2 -1 0 1 2 of 8 y + Automatic Zoom 1st differences 2nd differences This graph is described as concave down because it opens downward and ha a Vertex at (0,1). Since the parabola is concave down, the maximum value of the curve is found at the vertex. The maximum value is the y-value at the vertex.
Transcribed Image Text:1. Use the following equations to create a table of values (sub each x value into the equation to find the y value), calculate first and second differences, state vertex and direction of concave. Check each graph on desmos. y=-x² +1 (a = -1, b = 0, c = 1) X -2 -1 0 1 2 of 8 y + Automatic Zoom 1st differences 2nd differences This graph is described as concave down because it opens downward and ha a Vertex at (0,1). Since the parabola is concave down, the maximum value of the curve is found at the vertex. The maximum value is the y-value at the vertex.
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