Answer:
4948
Step-by-step explanation:
volme of a cylinder= π×h
what is y= - 2 (x-5) ^ 2 + 3 vertex, axis of symmetry, direction of opening, max or min and y intercept
1 answer:
Answer:
- vertex: (5, 3)
- axis of symmetry: x = 5
- direction of opening: downward
- max: y = 3
- y-intercept: -47
Step-by-step explanation:
Most of the questions can be answered by comparing the given equation to vertex form.
<h3>Vertex form</h3>The vertex form of the equation for a parabola is ...
y = a(x -h)² +k
where 'a' is a vertical scale factor, and (h, k) is the vertex. The sign of 'a' determines whether the parabola opens upward or downward.
<h3>Parameter values</h3>When we compare the given equation to the vertex form, we can easily see the values of 'a' and (h, k).
y = -2(x -5)² +3 . . . . . . . given equation
y = a(x -h)² +k . . . . . . . vertex form
The parameters are ...
a = -2, (h, k) = (5, 3)
We notice ...
- the sign of 'a' is negative
- the vertex is (5, 3)
The axis of symmetry is the vertical line through the vertex. It has the equation ...
x = h
x = 5 . . . . equation of the axis of symmetry
<h3>Direction of opening, max</h3>The sign of 'a' is negative. This means that large x-values will result in large negative y-values. The parabola opens downward.
When the curve opens <em>downward</em>, it means <em>the vertex is the highest point</em> on the curve. The maximum is the y-value of the vertex: k. There is no minimum.
The maximum is y = 3.
<h3>Y-intercept</h3>The y-intercept is where the graph crosses the y-axis. It can be found by setting x=0, and computing the value of y:
y = -2(0 -5)² +3
y = -2(25) +3 = -50 +3
y = -47 . . . . the y-intercept.
The ordered pair for the point there is (0, -47).
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We show the graph so you can see how these features relate to the shape of the graph and points on it.
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Answer:
Step-by-step explanation:
If you want to determine the domain and range of this analytically, you first need to factor the numerator and denominator to see if there is a common factor that can be reduced away. If there is, this affects the domain. The domain are the values in the denominator that the function covers as far as the x-values go. If we factor both the numerator and denominator, we get this:
Since there is a common factor in the numerator and the denominator, (x + 3), we can reduce those away. That type of discontinuity is called a removeable discontinuity and creates a hole in the graph at that value of x. The other factor, (x - 4), does not cancel out. This is called a vertical asymptote and affects the domain of the function. Since the denominator of a rational function (or any fraction, for that matter!) can't EVER equal 0, we see that the denominator of this function goes to 0 where x = 4. That means that the function has to split at that x-value. It comes in from the left, from negative infinity and goes down to negative infinity at x = 4. Then the graph picks up again to the right of x = 4 and comes from positive infinity and goes to positive infinity. The domain is:
(-∞, 4) U (4, ∞)
The range is (-∞, ∞)
If you're having trouble following the wording, refer to the graph of the function on your calculator and it should become apparent.