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, f(x) = a symmetric parabola, whose vertex is the point, and comparing with the standard equation,
In Exercises 1–6, find the domain and range of each function.1. ƒ(x) = 1 + x2 2. ƒ(x) = 1 - 2x3. F(x) = sqrt(5x + 10) 4. g(x) = sqrt(x2 - 3x)5. ƒ(t) = 4/3 - t6. G(t) = 2/t2 - 16
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
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Exercises 1-6: Identify f as being linear, quadratic, or
neither. If f is quadratic, identify the leading coefficient a
and evaluate f(-2).
1. f(x) = 1 – 2x + 3x? 2. f(x) = -5x + 11
3. f(x) = -
x
4. f(x) = (x² + 1)²
5. f(x) = } - *
6. f(x) = }r?
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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