Order Liner and Quadradic Functions

Order Liner and Quadradic Functions
Order 5894023
Order Liner and Quadradic Functions
Linear Functions
For questions 166 to 170, (a) find the x-intercept(s) and y-intercept for the graph
of f and (b) state the zero(s) of f. Refer to the following guidelines, as needed.
The graph of a linear function f defined by f(x) = mx b with m ≠ 0 is a straight
line with slope m that has exactly one x-intercept, , and exactly one yintercept, b. To determine the zeros of a function, find all values x for which f(x)
= 0. For f(x) = mx b with m ≠ 0, the x-intercept, , is the only zero of f.
166. f(x) = 3x 5
167.
168. f(x) = 10
169. f(x) = 0
170. f(x) = –2x – 5
For questions 171 and 172, suppose f is a linear function whose graph contains
the given point and has slope m. Write the equation y = mx b that defines f.
171.
172. m = –4, (–5,2)
For questions 173 and 174, suppose f is a linear function whose graph contains
the given points. Write the equation y = mx b that defines f.
173. (–2,11), (4,–1)
174. (4,6), (–10,6)
Linear Equations and Inequalities
For questions 175 to 179, refer to the following guidelines, as needed.
Steps for Solving One-Variable Linear Equations
1. Remove grouping symbols, if any, and then simplify.
2. (optional) Eliminate fractions, if any, by multiplying both sides of the
equation by the least common denominator of all the fractions in the
equation; and then simplify.
Order Liner and Quadradic Functions
3. Isolate the variable to one side of the equation, and then simplify.
4. If necessary, factor the side containing the variable so that one of the factors
is the variable.
5. Divide both sides by the coefficient of the variable.
Note: You can combine steps and/or mentally complete steps; however, be
careful when doing so because careless mistakes might occur.
175. Solve x 3(x – 2) = 2x – 4 for x.
176. Solve z for z.
177. Solve for x.
178. Solve Ax By = C for y. Write the answer in slope-intercept form.
179. Solve for y.
For questions 180 to 182, solve the linear inequality. Recall the following
guideline as you work.
In solving linear inequalities proceed as you do with linear equations EXCEPT
when you multiply or divide both sides by a negative number, reverse the
direction of the inequality symbol.
180. 3x 2 > 6x – 4
181. 3x – 2 ≤ 7 – 2x
182.
Quadratic Functions
In questions 183 to 185 for the function given, find (a) the y-intercept, and (b)
the number of x-intercepts. Refer to the following guidelines, as needed.
The graph of f(x) = ax
2 bx c, a ≠ 0, is a parabola (see Chapter 11 for a
discussion of general parabolas) that has a y-intercept at c and x-intercepts at the
real zeros (if any) of f. The zeros of f are the roots of the quadratic equation ax
2
bx c = 0. The discriminate b
2 – 4ac of the quadratic equation gives you three
possibilities for real zeros of f and thereby the x-intercepts: If b
2 – 4ac > 0, there
are two real unequal zeros and, therefore, two x-intercepts; if b
2 – 4ac = 0, there
is one real zero and, therefore, exactly one x-intercept; or if b
2 – 4ac 0, the parabola that is the graph f(x) = ax
2 bx c opens
(downward, upward); and if a < 0, the parabola opens (downward,
upward).
(B) When the leading coefficient of a quadratic function is negative, the ycoordinate of the vertex is the absolute (maximum, minimum) value of
f.
(C) When the leading coefficient of a quadratic function is positive, the ycoordinate of the vertex is the absolute (maximum, minimum) value of
f.
In questions 193 to 196, for the graph of the given quadratic function, (a) state
whether the parabola opens upward or downward, (b) find the vertex, (c) find the
axis of symmetry, (d) find the extremum, (e) state the domain and range, and (f)
state the intervals on which f is increasing or decreasing.
193. f(x) = x
2 – 12x 5
194. f(x) = x
2 4
195. g(x) = –3(x 1)
2 – 7
196. g(x) = –x
2 10x 3
Quadratic Equations and Inequalities
When solving quadratics by factoring, refer to the following formulas, as
needed.
acx
2 (ad bc)x bd = (ax b)(cx d) General trinomial
x
2 2xy y
2 = (x y)
2 Perfect square
x
2 – y
2 = (x y)(x – y) Difference of two squares
x
2 y
2 = (x yi)(x – yi) Sum of two squares
Note: Recall that i
2 = –1.
197. Solve x
2 – x – 6 = 0 by factoring.
198. Solve x
2 6x – 1 = – 5 by completing the square.
199. Solve 3x
2 – 5x 1 = 0 by using the quadratic formula.
For questions 200 to 202, solve using any preferred method.
200. x
2 – 3x 2 = 0
201. 9x
2 18x – 17=0
202. 6x
2 – 12x 7 = 0
For questions 203 to 207, solve the quadratic inequality. Write the solution set in
interval notation. Refer to the following guidelines, as needed.
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