# Finding X-Intercepts

• September 28th 2011, 10:22 AM
ArcherSam
Finding X-Intercepts
Hey

Please help me understand how to solve the problem below. This one question stopped me from getting a hundred on the test! Thanks

Problem:

Given the function f(x) = x^2 + 2x - 99, list the x-intercepts, if any, of the graph of f.

My attempt:

f(x) = x^2 + 2x - 99
y = x^2 + 2x - 99
0 = x^2 + 2x - 99
99 = x^2 + 2x
99 - 2x = x^2
sqrt(99 - 2x) = x
(99 - 2x) / x = x
99 - 2 = x
97 = x
x-intercept is (97, 0)

Sam
• September 28th 2011, 10:24 AM
e^(i*pi)
Re: Finding X-Intercepts
Quote:

Originally Posted by ArcherSam
Hey

Please help me understand how to solve the problem below. This one question stopped me from getting a hundred on the test! Thanks

Problem:

Given the function f(x) = x^2 + 2x - 99, list the x-intercepts, if any, of the graph of f.

My attempt:

f(x) = x^2 + 2x - 99
y = x^2 + 2x - 99
0 = x^2 + 2x - 99

Good work

Quote:

99 = x^2 + 2x
99 - 2x = x^2
sqrt(99 - 2x) = x
(99 - 2x) / x = x
99 - 2 = x
97 = x
x-intercept is (97, 0)

Sam
Your mistake is where I have bolded it - You have introduced a square root and then forgotten about it in the next step!

Instead you should try and factor it: what two numbers multiply to -99 and add to 2?

Hint: consider the factors of 99
• September 29th 2011, 10:06 AM
Deveno
Re: Finding X-Intercepts
or you could use the time-honored method of "completing the square":

$x^2 + 2x - 99 = 0$
$x^2 + 2x = 99$
$x^2 + 2x + 1 = 100$
$(x + 1)^2 = 10^2$
• September 29th 2011, 12:31 PM
masters
Re: Finding X-Intercepts
Quote:

Originally Posted by Deveno
or you could use the time-honored method of "completing the square":

$x^2 + 2x - 99 = 0$
$x^2 + 2x = 99$
$x^2 + 2x + 1 = 100$
$(x + 1)^2 = 10^2$

or

$x^2+2x-99=0$

$(x+11)(x-9)=0$ as "-1" suggested.
• October 11th 2011, 06:08 AM
ArcherSam
Re: Finding X-Intercepts
@master

Sorry for the late reply. I have been very busy. Overtime we have went over the four methods for solving quadratic equations(completing the square, square root method, factoring, and quadratic equation), which were taught after the test; (Rofl).