Answer:
a. opens: upward
b. a.o.s.: x = 1
c. vertex: (1, -4)
d. x-intercepts: (-1, 0), (3, 0); y-intercept: (0, -3)
Step-by-step explanation:
<h3><u>A:</u></h3>
By looking at the graph, we can see that the parabola opens upward. This means that its a-value is positive.
<h3><u>B:</u></h3>
The axis of symmetry is the line that passes exactly through the center of the parabola. It always starts with x = __, because it is a vertical line.
The center of this parabola is at the x-value of 1, so we can say that the equation of the axis of symmetry is x = 1.
<h3><u>C:</u></h3>
The vertex is at the highest or lowest point of the parabola, also known as the maximum or minimum point. Since this graph opens up, the vertex is at the minimum point.
Look at the graph and find the point where the parabola opens upwards. This point is at the x-value of 1 and the y-value of -4, so the vertex of the parabola is at (1, -4).
<h3><u>D:</u></h3>
Again, look at the graph provided to find the x and y-intercepts. On the x-axis, the parabola crosses through at the x-values of -1 and 3, so the x-intercepts are (-1, 0) and (3, 0).
The parabola crosses the y-axis at the y-value of -3, so the y-intercept of the parabola is (0, -3).
Answer:
C
Step-by-step explanation:
The profit (in thousands of dollars) of a company is given by the function:

And we want to find the maximum profit of the company.
Since the function is a quadratic with a negative leading coefficient, the maximum profit will occur at its vertex. Recall that the vertex of a quadratic is given by:

Find the <em>x-</em>coordinate of the vertex. In this case, <em>a</em> = -8, <em>b</em> = 32, and <em>c</em> = 14. Hence:

To find the maximum profit, substitute this value back into the function. Hence:

Therefore, the maximum profit of the company is 46 thousand dollars.
Our answer is C.
Answer:
48
Step-by-step explanation:
Plug in 16 to the function:
f(16)=1/3(4-16)^2
=1/3(-12)^2
=144(1/3)
=48
Answer:
She will get who is spending the most time and how much time from one person.
Step-by-step explanation:
How many of you spend time on musical instruments, and how much of it?