Rewrite the function by completing the square f(x) =4x2+12x+9
1 answer:
Answer:
see explanation
Step-by-step explanation:
Given
f(x) = 4x² + 12x + 9
The coefficient of the x² term must be 1 so factor out 4 from the first 2 terms
f(x) = 4(x² + 3x) + 9
To complete the square
add/ subtract ( half the coefficient of the x- term)² to x² + 3x
f(x) = 4(x² + 2()x +
-
) + 9
= 4(x + )² - 9 + 9
= 4(x + )²
Thus
f(x) = 4x² + 12x + 9 = 4(x + )²
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Answer:
<u>Part c) </u>
The Slope of the line is: m=-50 and represents the amount of money spent per week.
<u>Part d) </u>
The y-intercept is: c=300 and represents the maximum money we have that can be spend over the weeks (i.e. our maximum budget alowed).
Step-by-step explanation:
To solve this question we shall look at linear equations of the simplest form reading:
Eqn(1).
where:
: is our dependent variable that changes as a function of x
: is our independent variable that 'controls' our equation of y
: is the slope of the line
: is our y-intercept assuming an
⇔
relationship graph.
This means that as changes so does
as a result.
<u>Given Information: </u>
Here we know that $300 is our Total budget and thus our maximum value (of money) we can spend, so with respect to Eqn (1) here:
The budget of $50 here denotes the slope of the line, thus how much money is spend per week, so with respect to Eqn (1) here:
So finally we have the following linear equation of:
Eqn(2).
Notice here our negative sign on the slope of the line. This is simply because as the weeks pass by, we spend money therefore our original total of $300 will be decreasing by $50 per week.
So with respect to Eqn(2), and different weeks thus various values we have:
Week 1: we have
dollars.
Week 2: we have
dollars.
Thus having understood the above we can comment on the questions asked as follow:
<u>Part c) </u>
The Slope of the line is: and represents the amount of money spent per week.
<u>Part d) </u>
The y-intercept is: and represents the maximum money we have that can be spend over the weeks (i.e. our maximum budget alowed).