The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.
2 answers:
To convert the given quadratic equation into vertex form, one must recognize that a quadratic equation structured as 
can be expressed in vertex form as: 
. The vertex represents the peak or the lowest point of the parabola, which is given by: 
. Let’s denote: 
, and then we will proceed with the following steps to obtain the vertex form:
Step 1:
We extract the common factor from the first two terms of the equation:
Step 2:
Next, we will complete the square:
We take half of the coefficient of the term 
, square it, which gives:
At this stage, we have:
Step 3:
Now we simplify:
Step 4:
Finally, we factor:
Thus, 
The vertex form of the equation is: , and the vertex is
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<span>Which formula can be applied to find the side length of the rhombus?
The correct answer is the first choice: 10/Cos(30°)
Explanation:
1. The figure shows a right triangle, where the hypotenuse is denoted by "x," and this is the length you are solving for. Therefore, you have:
Cos(</span>α)=Adjacent side/Hypotenuse
<span>
</span>α=30°
<span> Adjacent side=(20 in)/2=10 in
Hypotenuse=x
2. Inputting these numbers into the equation yields:
</span>
Cos(α)=Adjacent side/Hypotenuse
<span> Cos(30°)=10/x
3. Hence, by isolating the hypotenuse "x," you arrive at the expression to find the side length of the rhombus, as shown below:
x=10/Cos(30°)
</span>
The correct answer is the first choice: 10/Cos(30°)
Explanation:
1. The figure shows a right triangle, where the hypotenuse is denoted by "x," and this is the length you are solving for. Therefore, you have:
Cos(</span>α)=Adjacent side/Hypotenuse
<span>
</span>α=30°
<span> Adjacent side=(20 in)/2=10 in
Hypotenuse=x
2. Inputting these numbers into the equation yields:
</span>
Cos(α)=Adjacent side/Hypotenuse
<span> Cos(30°)=10/x
3. Hence, by isolating the hypotenuse "x," you arrive at the expression to find the side length of the rhombus, as shown below:
x=10/Cos(30°)
</span>
The recipe uses 
cups of white flower together with 6 cups of wheat flower.
Therefore, the combined quantity of flower equals
If
represents that combined amount, the equation to write is:
Constraints are as follows:
y can only be
6
Note that if y = 0 then x would have to be -6, which is not possible.
Therefore, the combined quantity of flower equals
If
Constraints are as follows:
y can only be
Note that if y = 0 then x would have to be -6, which is not possible.