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:
4(25) - 9² = 100-81 = 19
Step-by-step explanation:
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Answer:
Step-by-step explanation:
Here we are given two coordinates through which our lines passes through. Now we are going to use the two point form to find the equation of the line.
The two point form is given as
Here we are given two coordinates . Thus replacing them in the formula and simplifying it will give us the equation of the line.
adding x and 6 on both sides we get
Hence this is our equation of the line passing through (5,6) & (4,7)
Answer:
True
Explanation:
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Answer:
4.91666666667
Step-by-step explanation:
1 1/3 + 1 5/6 + 1 3/4 = 4.91666666667
