Notice that the given equation is a parabola.
a) VERTEX
We need to find out where the parabola opens. You can predict the equation by tabulating any values of x and f(x). The table is shown:
x f(x)
_____
0 -7
1 -2
2 1
3 2
4 1
5 -3
As you plot it, the parabola opens downward. The vertex is (3,2) because that is the maximum point. The rest of the values are lesser than 2.
However, there is an easier technique to find the opening parabola and vertex rather than you plot it.
b) AXIS OF SYMMETRY
The axis of symmetry is a line that divides the parabola into two congruent halves. There is a formula for the axis of symmetry which is x = -b/2a.
Note: That is only applied if the parabola opens upward or downward and their axis of symmetry is a vertical line.
To get a and b, arrange the given equation first.
f(x) = -(x - 3)^2 + 2
= -(x^2 - 6x + 9) + 2
= -x^2 + 6x - 7 + 2
= -x^2 + 6x -5
The general form of the quadratic equation is ax^2 + bx + c. Setting a = -1, b = 6, c = -5, the axis of symmetry is
x = -6/(2*-1) = 3.
But anyway, you find it out the table above. We know that the coordinate of the vertex is (3,2). For instance, that is x = 3.
c) MAXIMUM or MINIMUM
Remember that the maximum refers to a vertex where the parabola opening downward. Otherwise, it is a minimum if the parabola opens upward. The maximum or minimum must have a certain value.
We know the answer will be a maximum. Since the axis is symmetry is a vertical line, the value for a maximum is 2.
d) DOMAIN and RANGE
Based on the given equation, the domain will be (-∞, ∞) because all values of x, the parabola continually spreads out.
The range will be (-∞, 2] because the maximum point is 2 and the rest of the values goes negative.
First, you would need to create an equation for this problem. Let x represent the number of sales made.
$100 + $3x = $160
Next, you would need to isolate the x.
Subtract $100 from both sides.
$3x = $60
Now, all you would need to do is divide both sides by $3.
x = 20
You would need to make at least 20 sales.
I hope this helps!
It’s D y=2x-8
multiple 2 by 3 and then you will get 6 and subtract 6 from -2 and you will get 8
so 8 will be your y intercept
Hello from MrBillDoesMath!
Answer:
x^2 - 2 x - 15
Discussion:
(
x - (-3)) * ( x- 5) =
(x +3) (x-5) =
x^2 - 2 x - 15
It is a concave upward curve (looks like a "u") as the x^2 term causes the function to grow larger as x approaches +\- infinity.
Thank you,
MrB
Answer:
The numbers are 2 and 3.
Step-by-step explanation:
The smaller number would have been 1 less than the bigger number so that if for example the smaller number is 1 and the bigger number is 2, their difference would have been 1-2 = -1
5 is an odd number so if it were to be divided into two integers, one would be more than the other, namely 2 and 3.
If you double-check their difference:
2-3 = -1
Thus, the two numbers are 2 and 3.
