Answer:
- f(x) = 2x(x -4)
- f(x) = 2(x -2)² +(-8)
Step-by-step explanation:
The factors of the factored form of the equation for the quadratic can be found by reading the x-intercept from the graph. The vertex form can be found by reading the coordinates of the vertex. The leading coefficient can be found any of several ways.
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<h3>factored form</h3>
The graph crosses the x-axis at x=0 and x=4. For x-intercept 'p', (x -p) is a factor. The leading coefficient can be found by matching the function value to a point on the graph somewhere other than at an x- or y-intercept.
If we choose to match the value at x=2, we must have f(2) = -8.
f(2) = a(x)(x -4) = a(2)(2 -4) = -8
-4a = -8 . . . . simplify
a = 2 . . . . . divide by -4
The factored form is ...
f(x) = 2(x)(x -4)
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<h3>vertex form</h3>
We can read the vertex from the graph as (2, -8). We note that 1 unit either side of the vertex, the graph rises 2 units, to (1, -6) and (3, -6). This tells us the leading coefficient is a=+2.
The vertex form equation is ...
f(x) = a(x -h)² +k
where the vertex is (h, k) and 'a' is the leading coefficient. For the values we read from the graph, the vertex-form equation is ...
f(x) = 2(x -2)² +(-8)
The expressions in the order that they would appear on a number line from least to greatest will be C. 17 over 9, square root of 6, square root of 15, square root of 30, 3 to the power of 3
<h3>How to calculate the expression?</h3>
17/9 = 1.89
✓30 = 5.47
✓6 = 2.45
✓15 = 3.87
3³ = 27
Therefore, the expressions in the order that they would appear on a number line from least to greatest will be 17 over 9, square root of 6, square root of 15, square root of 30, 3 to the power of 3.
In conclusion, the correct option is C.
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Answer:
Logarithmic
Step-by-step explanation:
It's literally a logarithmic function because it includes "log" which is short for logarithmic.
Answer:
c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean
Step-by-step explanation:
In a normal distribution, the shape is bell-shaped; this means it is symmetric.
The area under a normal distribution will always be equal to 1.
The mean, median and mode in a normal distribution are equal.
However, the data assumes values within 1 standard deviation above or below the mean 68% of the time, not 99.72% of the time. This is the characteristic that doesn't fit.