college algebra homework help?

Question

Need help with a few problems for my college algebra class, if you could help me by breaking them down that wud be great =)

Let f(x) = x^2 = 2x - 3
a.) f(a-1)

b.) f(-b)

State the equation of the circle in standard form having:

c.) center (1,3) passing through (5,6)

d.) Find the slope and y-intercept of 4x-3y= - 12

e.) write the equation g(x) that is the graph of f(x) = Square roote of x shifted 1 units and down 2 unit

f.) Find the equation of the line that passes through (2,3) and is (i) parallel and (ii) perpendicular to the line 2x-y=3

if you could answers any of these questions by breaking it down that would help me trememdously as im studying for a test.

correction for a.) f(x) = x^2 = 2x - 3 Simplify!

a. correction f(x) = x^2 + 2x - 3 simplify

e. correction shifted right 1 unites and down 2 units

Answer 1

a. f(a-1) = (a-1)² - 2(a-1) - 3
f(a-1) = a² - 2a + 1 - 2a + 2 - 3
f(a-1) = a² - 4a

b. f(-b) = (-b)² - 2(-b) - 3 = b² + 2b - 3

c. distance² between (1,3) and (5,6) is 4² + 3² = 25, so
(x-1)² + (y-3)² = 25

d. slope of ax + by = c is -a/b, and y intercept is c/b, so just reading the equation, slope is 4/3 and y intercept is 4

e. you didn't say whether 1st shift is left or right. if left, g(x) = √(x+1) - 2; if right, g(x) = √(x-1) - 2

f. parallel to 2x - y = k through (2,3) is
2x - y = 2(2) - (3) = 1
perpendicular is x + 2y = 2 + 2(3) = 8
notice I got the negative reciprocal slope by reversing the x and y coefficients and the sign between. simple.

Answer 2

I am going to assume here that f(x) = x^2 - 2x - 3
a. f(a-1) = (a-1)^2 - 2(a-1) - 3
=a^2 - 2a + 1 -2a + 2 - 3
=a^2 - 4a



b. f(-b) = (-b)^2 - 2 * (-b) - 3
= b^2 + 2b - 3



c. First find the radius using the pythagorean formula.
(6 - 3)^2 + (5 - 1)^2 = r^2
3^2 + 4^2 = r^2
9 + 16 = r^2
25 = r^2
r = 5

(x - 1)^2 + (y - 3)^2 = 25



d. 3y = 4x + 12
y = (4/3)x + 4

The slope is 4/3 and the y-intercept is at (0,4)



e. f(x) = sqrt(x)
You don't say which way the x is shifted, but let's assume it is to the right.

Some points on f are (0,0), (1,1), (4,2), (9,3)
Some points on g are (1, -2), (2, -3), (5, 0), (10,1)
g(x) = (x-1)^2 - 2



f. y = 2x - 3
The slope is 2. A line parallel will have a slope 2 and a line perpendicular with have a slope -1/2

y = 2x + b
3 = 2 * 2 + b
3 = 4 + b
b = -1

y = 2x - 1

y = (-1/2) * x + b
3 = (-1/2) *2 + b
3 = -1 + b
b = 4

y = (-1/2) *x + 4

Answer 3

I don't know how the first problem is done!!!?
c) Equation: (x-h)^2+(y-k)^2=r^2
where center is at (h,k) and r is the radius
First use the distance formula to get r.
r = sqrt((1-5)^2+(3-6)^2=5
So you will have,
(x-1)^2+(y-3)^2=25
x^2+y^2-2x-6y-15=0

d) write in slope intercept form:
3y=4x+12
y=4/3x+4, where slope=4/3 and y-intercept is 4

I'm about to sleep, hope you can work out the rest. Goodluck.

Answer 4

.29 is a hundred% in view it quite is your beginning element, a hundred% is likewise =a million=.29/.29, so .174 on the concern of .29 is .174/.29. The ratio simplified is .6 so he's barely 60% as sturdy, making a 40% cut back