Question

help

Answer 1

@oliver69

Answer 2

what equation has a graph tip parabola ?

Answer 3

Well we know it's a negative. Down is negative up is positive.

Answer 4

@jhonyy9

Answer 5

tbh im not that good at math

Answer 6

Okay so we know the vertex is (0,0) because it crosses both the x and y axis.

We know it's negative because it's facing down.

Further steps:

The equation of a parabola is \[y=\frac{ 1 }{ 4(f−k)}(x−h)^2+k\] , where (h,k)(h,k) is the vertex and (h,f)(h,f) is the focus.

Thus, h=0, k=0

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix: f−k=k−3/4​

Solving the system {h=0, k=0, f−k=k−3/4

⎧​h=0
{k=0
{f−k=k−43​​, we get that h=0, k=0, f=−3/4

The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: x=0

The focal length is the distance between the focus and the vertex: 3/4​.

The focal parameter is the distance between the focus and the directrix: 3/2​.

The latus rectum is parallel to the directrix and passes through the focus: y=−3/4

The endpoints of the latus rectum can be found by solving the system
{x^2+3y=0
{y=−3/4

The endpoints of the latus rectum are (−3/2,−3/4)(−2/3​,−4/3​)

The length of the latus rectum (focal width) is four times the distance between the vertex and the focus: 3.

The eccentricity of a parabola is always 1

The x-intercepts can be found by setting y=0y=0 in the equation and solving for x

x-intercept: (0,0)

The y-intercepts can be found by setting x=0x=0 in the equation and solving for y:

y-intercept: (0,0)

There for your answer should be y = \[-\frac{ x^2 }{ 3}\]

Answer 7

I hope I could help

Answer 8

hm

Answer 9

thank you I got it