Find equation of parabola in standard form that passes through points (7,4) and (13,-2) and has a axis of y=2?

Answer 1

x= -.5y^2+15

Since axis are y=2 we have x=ay^2+c
Using points given we have a system of 2 equations

13 = a(-2)^2 + c
7 = a(4)^2 + c

13 = 4a + c
7 = 16a + c
We have
6 = -12a or a = -.5
then c=15

we have

x= -.5y^2 + 15

Answer 2

The form of the parabola that has the axis in it is

y = a (x-axis)^2 + b

I'm assuming, perhaps incorrectly that the axis is x=2 since that is how it's normally written. We know the axis is 2 and we know two points (7,4) and (13,-2) so we get the following two equations in two variables.

4 = a (7-2)^2 + b = 25a + b
-2= a (13-2)^2 + b = 121a + b

If you subtract the second equation from the first you get

6 = -96 a ......... a = -1/16

Plug back in to one of the equations and solve for b, b=89/16
This makes the final equation

y = -1/16 ( x-2 )^2 + 89/16

You might want to convert this to y = ax^2 + bx + c depending on your teacher.

Answer 3

eqn of parabola with axis y=0 is y^2 = 4ax

since axis is y = 2, let the equation be (y - 2)^2 = ax +b

substituting the points (7,4) and (13,-2) we get

4 = 7a +b and
16 = 13a + b

solving a = 2 and b = -10

so required equation is (y - 2)^2 = 2x -10

Answer 4

if by "has a axis of y = 2" you mean passes through (0,2), then

y = ax^2 + bx + c

4 = a(7)^2 + b(7) + 2
4 = 49a + 7b + 2
49a + 7b = 2

-2 = a(13)^2 + b(13) + 2
-2 = 169a + 13b + 2
169a + 13b = -4

49a + 7b = 2
169a + 13b = -4

Multiply top by -13 and bottom by 7

-637a - 91b = -26
1183a + 91b = -28

546a = -54
a = -9/91

49a + 7b = 2
49(-9/91) + 7b = 2
(-441/91) + 7b = 2
7b = 2 + (441/91)
7b = (182/91) + (441/91)
7b = (182 + 441)/91
7b = (623/91)
b = (623/637)
b = (89/91)

y = (-9/91)x^2 + (89/91)x + 2

Thats the general form

y = (-9/91)x^2 + (89/91)x + 2
y = ((-9/91)x^2 + (89/91)x) + 2
y = (-9/91)(x^2 - (89/9)x) + 2
y = (-9/91)(x^2 - (89/9)x + (7921/324) - (7921/324)) + 2
y = (-9/91)((x^2 - (89/9)x + (7921/324)) - (7921/324)) + 2
y = (-9/91)(x^2 - (89/9)x + (7921/324)) + (7921/3276) + 2

y = (-9/91)(x^2 - (89/9)x + (7921/324)) + (7921/3276) + (6552/3276)

y = (-9/91)(x^2 - (89/9)x + (7921/324)) + ((7921 + 6552)/3276)
y = (-9/91)(x^2 - (89/9)x + (7921/324)) + (14473/3276)
y = (-9/91)((324x^2 - 3204x + 7921)/324) + (14473/3276)
y = (-9/91)((1/324)(324x^2 - 3204x + 7921)) + (14473/3276)
y = (-9/29484)(324x^2 - 3204x + 7921) + (14473/3276)
y = (-1/3276)(324x^2 - 3204x + 7921) + (14473/3276)
y = (-1/3276)(18x - 89)^2 + (14473/3276)

In Standard form, and assuming you meant for it to have a y-intercept of 2, then

y = (-1/3276)(18x - 89)^2 + (14473/3276)
or
y = (-1/3276)((18x - 89)^2 - 14473)

but i would leave it at y = (-1/3276)(18x - 89)^2 + (14473/3276)

Answer 5

y={(square root of) [(x-10)/2]}+2

or

y=[(square root of) (.5x-5)]+2