A parking lot has 916 parking spaces that are shaped like parallelograms. The base of each space is 10 feet, and the height of e
2 answers:
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The equation of the quadratic function is f(x) = x²+ 2/3x - 1/9
<h3>How to determine the quadratic equation?</h3>From the question, the given parameters are:
Roots = (-1 - √2)/3 and (-1 + √2)/3
The quadratic equation is then calculated as
f(x) = The products of (x - roots)
Substitute the known values in the above equation
So, we have the following equation
This gives
Evaluate the products
Evaluate the like terms
So, we have
f(x) = x²+ 2/3x - 1/9
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Answer:
D
Step-by-step explanation:
We have the piecewise function:
And we want to find x such that f(x)=1.
So, let's substitute 1 for f(x):
This has two equations. So, we can separate them into two separate cases. Namely:
Let's solve for x in each case.
Case I:
We have:
Add 1 to both sides:
Let's cancel out the fraction by multiplying both sides by -2. So:
The right side cancels:
Flip:
So, x is -4.
Case II:
We have:
Flip:
This is the solution for our second case.
So, we have:
Now, can check to see if we have to to remove solution(s) that don't work.
Note that x=-4 is the solution to our first equation.
The first equation is defined only if x is less than -2.
-4 <em>is </em>less than -2. So, x=-4 is indeed a solution.
x=1 is the solution to our second equation.
The second equation is defined only if x is greater than or equal to -2.
1 <em>is</em> greater than or equal to -2. So, x=1 is <em>also </em>a solution.
Therefore, our two solutions are:
Out of our answer choices, we can pick D.
And we're done!