In Exercises 1–4, the graph of a quadratic function is given. Write the function’s equation, selecting from the following options: f ( x ) = ( x + 1 ) 2 − 1 , g ( x ) = ( x + 1 ) 2 + 1 , h ( x ) = ( x − 1 ) 2 + 1 , j ( x ) = ( x − 1 ) 2 − 1.
In Exercises 1–4, the graph of a quadratic function is given. Write the function’s equation, selecting from the following options: f ( x ) = ( x + 1 ) 2 − 1 , g ( x ) = ( x + 1 ) 2 + 1 , h ( x ) = ( x − 1 ) 2 + 1 , j ( x ) = ( x − 1 ) 2 − 1.
Solution Summary: The author explains the quadratic function's standard form of f, which is a parabola whose vertex is the point and symmetric with respect to the line.
In Exercises 17–27, use the vertex and intercepts to sketchthe 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.
17. f(x)=(x-4)2 -1
19. f(x)=(x-1)2 +2
21. y-1=(x-3)2
23. f(x)=2(x+2)2 -1
25. f(x)=4-(x-1)2
27. f(x)=x2 -2x-3
In Exercises 39–44, an equation of a quadratic function is given.
a. Determine, without graphing, whether the function has a
minimum value or a maximum value.
b. Find the minimum or maximum value and determine
where it occurs.
c. Identify the function's domain and its range.
39. f(x) = 3x – 12x – 1
41. f(x) = -4x² + &r – 3
43. f(x) = 5x? - 5x
40. f(x) = 2x? – &r – 3
42. f(x) = -2r² – 12x + 3
44. f(x) = 6x - 6x
%3D
%3D
%3D
In Exercises15–36, find the points of inflection and discuss theconcavity of the graph of the function.
f(x)=\frac{6-x}{\sqrt{x}}
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Interpreting Graphs of Quadratic Equations (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=BHgewRcuoRM;License: Standard YouTube License, CC-BY
Solve a Trig Equation in Quadratic Form Using the Quadratic Formula (Cosine, 4 Solutions); Author: Mathispower4u;https://www.youtube.com/watch?v=N6jw_i74AVQ;License: Standard YouTube License, CC-BY