Answer:
yx
Step-by-step explanation:
put 2 variables next to each other and it means multiply.
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.
Answer:
x = 9
Step-by-step explanation:
1. x - 2 * 5 = 35
2. 5 * 7 = 35
3. 9 - 2 = 7
4. 9 - 2 * 5 = 35
The answer is <span> B- y=4-1.5x
</span><span>David is rowing a boat upstream, so the river is slowing him down. Thus, the net speed is 6 mph - 2 mph = 4 mph.
Since David's speed </span><span>decreases at a rate of 1.5 miles per hour, after x hours his speed y will be:
y = 4 - 1.5 x</span>
A few ways. you can enter it into a calculator for one, but the easiest way would be to reference a unit circle and look for an ordered pair where sin (the y value), is equal to -1/2
on a unit circle, the sin value is -1/2 at 7pi/6 and 11pi/6
because sin is the y value, it will additionally be in the quadrants III or IV based on the fact that (-1/2) as a sin value IS a negative and would have to be found in a quadrant in which sin is negative (the lower half of a coordinate plane, in this case)
