Given three points
P1(-2,8)
P2(0,-4)
P3(4,68)
We need the quadratic equation that passes through all three points.
Solution:
We first assume the final equation to be
f(x)=ax^2+bx+c .............................(0)
Observations:
1. Points are not symmetric, so cannot find vertex visually.
2. Using the point (0,-4) we substitute x=0 into f(x) to get
f(0)=0+0+c=-4, hence c=-4.
3. We will use the two other points (P1 & P3) to set up a system of two equations to find a and b.
f(-2)=a(-2)^2+b(-2)-4=8 => 4a-2b-4=8.................(1)
f(4)=a(4^2)+b(4)-4=68 => 16a+4b-4=68.............(2)
4. Solve system
2(1)+(2) => 24a+0b-12=84 => 24a=96 => a=96/24 => a=4 ......(3)
substitute (3) in (2) => 16(4)+4b-4=68 => b=8/4 => b=2 ..........(4)
5. Put values c=-4, a=4, b=2 into equation (0) to get
f(x)=4x^2+2x-4
Check:
f(-2)=4((-2)^2)+2(-2)-4=16-4-4=8
f(0)=0+0-4 = -4
f(4)=4(4^2)+2(4)-4=64+8-4=68
So all consistent, => solution ok.
Hello!
This is a rectangular prism
To find the volume you use the equation whl
w is width
h is height
l is length
Put in the values
6.3 * 7.9 * 12.4 = 617.1
The answer is D
Hope this helps!
1. -35x+710 = -25x+570
-10x=-140
x=14
In 14 weeks, Pedro and Maria's accounts will have the same amount.
2. 9x+90 = 13x+50
-4x=-40
x=10
For 10 square yards of carpeting will the cost be the same for both stores.
3. 0.06x+44 = 0.09x+35
-0.09x= -9
x=100
For 100 miles both companies will charge the same price.
4. 15x+250 = 20x+200
-5x= -50
x= 10
It will take 10 weeks for the amount in each savings account to be the same.
5. 25x+250 = 50x
-25x = -250
x = 10
10 stereos must be sold to make the same amount of money under both plans.
Hope this helps!
The solution is
(2,1)
So the value of the x-coordinate is 2
Answer:
circumference = diameter * PI which is 3.14159 ...
circumference = 72 * 3.14159 ...
circumference = 226.19467 inches
Step-by-step explanation:
