I need help with this parabola question.
A parabola with the axis of symmetry in the yaxis passes through the points (1,4) and (3, 20). Determine its equation algebraically. Could someone give me some help, I havent seen a question like this before, Could you show your work please.
A parabola with the axis of symmetry in the yaxis passes through the points (1,4) and (3, 20). Determine its equation algebraically. Could someone give me some help, I havent seen a question like this before, Could you show your work please.

Ok, the best way I can think of to do a problem like this would be to think about the general equation of a parabola y=ax^2+bx+c. If the yaxis is a line of symmetry, then b must be 0. This makes sense because now the equation is just y= ax^2 +c. It's just a parabola moved up or down the yaxis by c places.
So now we can use the two points (1,4) and (3,20) to create two equations which we can solve simultaneously to find the values of a and c.
4 = a * 1^2 +c __________________ eqn 1
20 = a * (3)^2 +c ________________ eqn 2
eqn 2  eqn 1
24 = 8a
a = 3
substitute into equ 1 to find c:
c= 7
Therefore the equation of your parabola is y= 3x^2 +7
If you draw this on the computer or a calculator you'll see it does indeed go through (1,4) and (3, 20)
Hope that helped!
So now we can use the two points (1,4) and (3,20) to create two equations which we can solve simultaneously to find the values of a and c.
4 = a * 1^2 +c __________________ eqn 1
20 = a * (3)^2 +c ________________ eqn 2
eqn 2  eqn 1
24 = 8a
a = 3
substitute into equ 1 to find c:
c= 7
Therefore the equation of your parabola is y= 3x^2 +7
If you draw this on the computer or a calculator you'll see it does indeed go through (1,4) and (3, 20)
Hope that helped!

The general form of the equation of a parabola is
y = f(x) = ax² + bx + c.
Since (1,4) and (3, 20) belong to the parabola,
f(1) = 4 and f(3) = 20.
Hence the equations:
1a + 1b + 1c = 4 . . . (1)
9a − 3b + 1c = 20. . (2)
Since the parabola is symmetrical with respect to
the yaxis, f(x) = f(x) for all x, in particular f(1) = f(1).
Hence the equation
1a − 1b + 1c = 4 . . . (3)
Solving the system of equations (1), (2) and (3), we get
(a, b, c) = (3, 0, 7)
The equation of the parabola is
y = 3x² + 7
y = f(x) = ax² + bx + c.
Since (1,4) and (3, 20) belong to the parabola,
f(1) = 4 and f(3) = 20.
Hence the equations:
1a + 1b + 1c = 4 . . . (1)
9a − 3b + 1c = 20. . (2)
Since the parabola is symmetrical with respect to
the yaxis, f(x) = f(x) for all x, in particular f(1) = f(1).
Hence the equation
1a − 1b + 1c = 4 . . . (3)
Solving the system of equations (1), (2) and (3), we get
(a, b, c) = (3, 0, 7)
The equation of the parabola is
y = 3x² + 7

The equation of a parabola with the axis of symmetry in the yaxis is of the form
y = ax² + b
Since (1,4) is on the parabola,
4 = a(1)² + b = a + b
Since (3,20) is on the parabola,
20 = a(3)² + b = 9a + b
Solving 4 = a + b and 20 = 9a + b silmultaneously yields
a = 3
b = 7
So, y = 3x² + 7 is the equation you are looking for.
y = ax² + b
Since (1,4) is on the parabola,
4 = a(1)² + b = a + b
Since (3,20) is on the parabola,
20 = a(3)² + b = 9a + b
Solving 4 = a + b and 20 = 9a + b silmultaneously yields
a = 3
b = 7
So, y = 3x² + 7 is the equation you are looking for.

y = ax^2 + b
Plug in (1, 4) and (3, 20),
4 = a + b ......(1)
20 = 9a + b ......(2)
(2)(1): 24 = 8a
a = 3
b = 7
Answer: y = 3x^2 + 7
Plug in (1, 4) and (3, 20),
4 = a + b ......(1)
20 = 9a + b ......(2)
(2)(1): 24 = 8a
a = 3
b = 7
Answer: y = 3x^2 + 7