|
Question 823125: Find the value(s) of x in the domain of f(x)= -x^2+4x+1 for which f(x) = -4. Please show all work.
Thank you for your assistance.
Found 2 solutions by TimothyLamb, stanbon:
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
f(x) = -x^2 + 4x + 1
for f(x) = -4
-x^2 + 4x + 1 = -4
-x^2 + 4x + 5 = 0
---
the above quadratic equation is in standard form, with a=-1, b=4, and c=5
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-1 4 5
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
---
this quadratic has two real roots (the x-intercepts), which are:
x = -1
x = 5
---
negative length doesn't make sense for this problem, so use the positive root
---
answer:
distance from the bottom of the ladder to building = 3 m
distance from the ground to the top of ladder = 4 m
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Find the value(s) of x in the domain of f(x)= -x^2+4x+1 for which f(x) = -4.
------
Solve:
-x^2 + 4x + 1 = -4
------
-x^2 + 4x + 5 = 0
------
x^2 -4x - 5 = 0
Factor:
(x-5)(x+1) = 0
x = 5 or x = -1
====================
Cheers,
Stan H.
|
|
|
| |
