Respuesta :
Answer:
This is a contradiction, which means that the three points provided do not lie on the same parabola. Therefore, there is no unique parabola that passes through the points (0, 0), (-2, 4), and (2, 4).
Step-by-step explanation:
To find the equation of the parabola given the three points (-2, 4), (0, 0), and (2, 4), we'll use the standard form of the equation for a parabola:
y=a[tex]x^{2}[/tex] +bx+c
We have three points, so we can create three equations by substituting the coordinates of each point into the equation and solving the resulting system of equations for the coefficients
Let's start with the point (0, 0):
y=a(0)² + b(0) + c
0=c
Now, using the point (-2, 4):
y=a(−2)² +b(−2) + 0
4=4a−2b
And using the point (2, 4):
y=a(2)²+b(2) + 0
4=4a+2b
Now, we have a system of three equations:
0=c
4=4a−2b
4=4a+2b
We can solve this system of equations to find the values of a,b, and c.
From the second and third equations, we can see that 4a=2 and 2b=4. Solving these equations, we get a= 1/2 and b=2
Now, substituting a=1/2 and b=2 into any of the original equations, we can find c. Using 4=4a+2b, we have:
4=4(1/2)+2(2)
4=2+4
4=6
This is a contradiction, which means that the three points provided do not lie on the same parabola. Therefore, there is no unique parabola that passes through the points (0, 0), (-2, 4), and (2, 4).
