1. Consider the following points.(2, 9), (9, 2)a. Find the distance between the two points.b. Find the midpoint of the line segment containing the two points.atiothe ne possing through the points, Cve the slope of this ine.t2. Determine whether each point lies on the graph of the equation.y = x² – 4x + 3(-3, -24)3. Identify the x- and y-intercepts of the graph. Verify your results algebraically.y = 16 – 4x²h(-2)ch(x+1)- Use the algebraic tests to check for symmetry with respect to both axes and theorigin.x – y? = 4|Find all realvalues of x for whwhich )= 0,. Find the valuFind the slope and y-intercept (if possible) of the equation of the line. (If an answerdoes not exist, enter DNE.)a. x + 3 = 0%3Db. 14x - бу %3D 66

Answered: Determine whether e y = x2 - 4x + 3

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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1. Consider the following points.
(2, 9), (9, 2)
a. Find the distance between the two points.
b. Find the midpoint of the line segment containing the two points.
atio
the ne possing through the points, Cve the slope of this ine.
t
2. Determine whether each point lies on the graph of the equation.
y = x² – 4x + 3
(-3, -24)
3. Identify the x- and y-intercepts of the graph. Verify your results algebraically.
y = 16 – 4x²
h(-2)
ch(x+1)
- Use the algebraic tests to check for symmetry with respect to both axes and the
origin.
x – y? = 4
|
Find all real
values of x for wh
which )= 0,
. Find the valu
Find the slope and y-intercept (if possible) of the equation of the line. (If an answer
does not exist, enter DNE.)
a. x + 3 = 0
%3D
b. 14x - бу %3D 66

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$(1) (a) w e h a v e b e e n g i v e n t w o p o i n t s (2, 9) a n d (9, 2) w e h a v e t o f i n d t h e d i s \tan c e b e t w e e n t h e m . a s w e k n o w t h a t d i s \tan c e b e t w e e n t w o p o i n t s (x_{1}, y_{1}) a n d (x_{2}, y_{2}) i s g i v e n a s d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} d = \sqrt{{(9 - 2)}^{2} + {(2 - 9)}^{2}} d = \sqrt{{(7)}^{2} + {(- 7)}^{2}} d = \sqrt{49 + 49} d = 7 \sqrt{2} t h e r e f o r e d i s t a n c e b e t w e e n (2, 9) a n d (9, 2) i s 7 \sqrt{2} . (b) m i d p o i n t s o f t h e l i n e c o n t a i n g t h e t w o p o i n t s (2, 9) a n d (9, 2) i s l e t t h e c o o r d i n a t e s o f t h e m i d p o i n t s b e (x, y) t h e r e f o r e (x, y) = (\frac{2 + 9}{2}, \frac{2 + 9}{2}) (x, y) = (\frac{11}{2}, \frac{11}{2})$

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