# maths question help (1 Viewer)

#### chrstinee

##### Member
A satellite dish is in the shape of a parabola
with equation y = −3x^2 + 6, and all dimensions are in metres.

Find w, the width of the dish, to 1 decimal
place.

#### jimmysmith560

##### Phénix Trilingue

You need to find the roots by making y = 0

-3x^2 + 6 = 0
3x^2 - 6 = 0
x^2 - 2 = 0
x^2 = 2
x = +/- sqrt 2 (approximately -1.4 and 1.4).

The width of the satellite dish would then be the distance between the roots

w = 1.4 + 1.4 = 2.8 metres (1 decimal place)

Last edited:

#### chrstinee

##### Member
View attachment 30419

I think you need to find the roots by making y = 0 ?

-3x^2 + 6 = 0
3x^2 - 6 = 0
x^2 - 2 = 0
x^2 = 2
x = +/- sqrt 2 (approximately -1.4 and 1.4).

The width of the satellite dish would then be the distance between the roots?

w = 1.4 + 1.4 = 2.8 metres (1 decimal place)

Not 100% sure though.
omg thank you so much

#### CM_Tutor

##### Moderator
Moderator
@jimmysmith560's answer is correct and the question is badly written. For a start, a satellite dish is a three-dimensional object, and further it is finite, so saying it has an equation like the one given is problematic. The question should be re-written as something like:

A satellite dish is in the shape of a parabola rotated about its axis. With all distances in metres, a cross-section
of the dish through its vertex matches that part of $\bg_white y=-3x^2+6$ that is on or above the y-axis.
Find w, the width of the dish at its widest point, in exact form and to 1 decimal place.​

The answer would be $\bg_white w=2\sqrt{2}\ \text{m}\approx 2.8\ \text{m}$

#### jimmysmith560

##### Phénix Trilingue
@jimmysmith560's answer is correct and the question is badly written. For a start, a satellite dish is a three-dimensional object, and further it is finite, so saying it has an equation like the one given is problematic. The question should be re-written as something like:

A satellite dish is in the shape of a parabola rotated about its axis. With all distances in metres, a cross-section
of the dish through its vertex matches that part of $\bg_white y=-3x^2+6$ that is on or above the y-axis.
Find w, the width of the dish at its widest point, in exact form and to 1 decimal place.​

The answer would be $\bg_white w=2\sqrt{2}\ \text{m}\approx 2.8\ \text{m}$
Thank you!