Write the equation, in standard form, of the parabola containing the following points: (0,1), (1,5), (2,3) I know the answer is y=-3x^2+7x+1 but idk how to work it out pleaseee helpp :(
To find the equation of a parabola in standard form, you need three points on the parabola. Given the points (0,1), (1,5), and (2,3), we can use these points to form three equations and solve them simultaneously to determine the coefficients of the parabola.
Step 1: Assume the equation of the parabola to be in the form y = ax^2 + bx + c, where a, b, and c are constants.
Step 2: Plug in the x and y coordinates of the three given points into the equation from Step 1. This will yield three equations:
For the point (0,1):
y = a(0)^2 + b(0) + c
1 = 0 + 0 + c
c = 1
For the point (1,5):
y = a(1)^2 + b(1) + c
5 = a + b + 1
For the point (2,3):
y = a(2)^2 + b(2) + c
3 = 4a + 2b + 1
Step 3: Simplify the second and third equations:
5 = a + b + 1 --> a + b = 4
3 = 4a + 2b + 1 --> 4a + 2b = 2
Step 4: Solve the system of equations. Multiply the first equation by 2 to eliminate the b term:
2(a + b) = 2(4) --> 2a + 2b = 8
Subtract this equation from the third equation:
(4a + 2b) - (2a + 2b) = 2 - 8
2a = -6
a = -3
Substitute the value of a into the first equation to solve for b:
(-3) + b = 4
b = 4 + 3
b = 7
Step 5: Substitute the values of a, b, and c back into the equation y = ax^2 + bx + c:
y = (-3)x^2 + 7x + 1
Therefore, the equation of the parabola is y = -3x^2 + 7x + 1, as you mentioned.
again?
See your first post on this problem.