In Exercises 17-38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f ( x ) = 5 4 − ( x − 1 2 ) 2
In Exercises 17-38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f ( x ) = 5 4 − ( x − 1 2 ) 2
Solution Summary: The author explains the quadratic function and its axis of symmetry, domain, and range.
In Exercises 17-38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range.
Match the equation, graph, and description of transformation.
Horizontal translation 1
unit right; vertical
translation 1 unit up;
vertical shrink of 1/2;
reflection across the x
axis
Horizontal translation 1
unit left; vertical
translation 1 unit
down; vertical stretch
of 2
Horizontal translation
2 units right; reflection
across the x-axis
Vertical translation 1
unit up; vertical stretch
of 2; reflection across
the x-axis
Reflection across the x
- axis; vertical
translation 2 units
down
Horizontal translation
2 units left
Horizontal translation
2 units right
Vertical translation 1
unit down; vertical
shrink of 1/2; reflection
across the x-axis
Vertical translation 2
units down
Horizontal translation 1
unit left; vertical
translation 2 units up;
vertical stretch of 2;
reflection across the x
- axis
f(x) = -
=-½ ½ (x − 1)²+1
f(x) = x²-2
f(x) = -2(x+1)²+2
f(x)=2(x+1)²-1
f(x)=-(x-2)²
f(x)=(x-2)²
f(x) =
f(x) = -2x²+1
f(x) = -x²-2
f(x) = (x+2)²
What is the vertex, increasing interval, decreasing interval, domain, range, root/solution/zero, and the end behavior?
The augmented matrix of a linear system has been reduced by row operations to the
form shown. Continue the appropriate row operations and describe the solution set of the
original system.
1 -1
0 1 -2
00-4
0-6
0
0
1
- 3
3
0
001
4
Precalculus: Mathematics for Calculus (Standalone Book)
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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY