1. ## 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

2. ## Re: Finding X-Intercepts

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

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

3. ## Re: Finding X-Intercepts

or you could use the time-honored method of "completing the square":

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

4. ## Re: Finding X-Intercepts

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.

5. ## 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; .