quadratic functions: various questions

[Hielly]

heys need help on this question first

1.Use a CAS calculator to help answer the following questions.
A pole 11 metres high is firmly secured to the ground. A parabolic arch is to be
attached to the pole 3 metres above the ground as shown in the diagram below. A
metal rod will run directly from the top of the pole straight to the ground so that it just
touches the arch in one position only. Let y be the height above the ground in metres
and x be the distance along the ground from the foot of the pole in metres.

a)The arch is to be modelled by the quadratic equation y = -1/8x^2 + a/4x +3 , where a
is a non-zero positive constant. Find where the arch meets the ground in terms of
a, that is, find the x-intercept.

so we're trying to find A, the x point? not sure what to do

view attachment for picture

Thanks

edit: y=-1/8x^2 + a/4x +3

[Hielly]

ohh okay i was wondering if its possible to find A by hand?

[d0minicz]

use the quadratic formula and plug in the equation
you then use the positive solution

[Hielly]

i used the quadratic formula using a=-1/8 b=a/4 c=3 and it came out really messy

[Damo17]

i used the quadratic formula using a=-1/8 b=a/4 c=3 and it came out really messy

How did you get them values for a and b?

[Hielly]

oh woops the equation is meant to be y=-1/8x^2 + a/4x +3 ==" i copied and pasted it from the pdf.. without noticing that it didnt copy fractions. sigh

[d0minicz]

y = – x^2 + x + 3, where a
is a non-zero positive constant.

does that mean theres supposed to be an a in the quadratic equation?

[TrueTears]

y = – x^2 + x + 3, where a
is a non-zero positive constant.

does that mean theres supposed to be an a in the quadratic equation?

think hielly just edited her post

[d0minicz]

ooo yeah my bad lol

[Damo17]

what is the answer?

[Hielly]

okay so by using quadratic formula to solve it it came out with very small numbers, not sure if im correct though

answer is x=a + square root a^2 +25

[Damo17]

I get

[Hielly]

how did you get the answer damo ?

[Damo17]

Sorry for it being messy.

[Hielly]

okay one question how did the a^2 +24 / 16 turn into a^2 +24/4.,

sorry i have never encountered so many fractions while doing the quadratic formula