determine the equation of the parabola passing through the points (3,13), (0,1), and (1, 7)
Question
2 Answer

1. User Answers nnoorian13
Answer:
y=5x+1
Stepbystep explanation:
The equation is: y=mx+b
m = the slope of the line
b = the yintercept (0,b)
The yintercept is (0,1) so b = (0,1)
So the equation would be y =mx+1
Now in order to calculate the slope, the equation is:
y₂y₁ over
x₂x₁
So we should use the points (3,13) and (1,7).
713 over (over means a fraction symbol)
1+3
Simplify:
20 over 4 =5/1 = 5
M=5
So the equation is now:
y=5x+1

2. User Answers Luv2Teach
Answer:
Stepbystep explanation:
You need to do some solving simultaneously to get these values. Your quadratic equation is of the form
[tex]ax^2+bx+c=y[/tex]
Use the coordinates you've been given to solve 3 equations. It will be super simple if we start with the coordinate (0, 1). Here's why (obvious after some substitution is done):
[tex]a(0)^2+b(0)+c=1[/tex] which gives us that
c = 1. Now we have a variable to plug in for c to solve for a and b. Again, we have coordinates that we can use to create 2 more equations:
[tex]a(3)^2+b(3)+1=13[/tex] and, simplified:
9a  3b = 12
and the second equation is:
[tex]a(1)^2+b(1)+1=7[/tex] and, simplified:
a + b = 8
Now combine the 2 bold equations and solve by elimination or substitution to find either a or b. I chose elimination and multiplied the second equation by 3 to get a new equation:
3a + 3b = 24
Using the elimination method:
9a  3b = 12
3a + 3b = 24
You can see that the b's subtract each other away, leaving us with
12a = 12 so
a = 1
Now plug 1 in for a to solve for b:
1 + b = 8 so
b = 7 and the quadratic is
[tex]x^27x+1=y[/tex]