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3 years ago

The vertex of this parabola is at (-2, 5). Which of the following could be its equation?

Mathematics

1 answer:

LenKa [72]3 years ago

5 0

Answer:

y=3(x+2)^2+5

Step-by-step explanation:

The vertex is (p, q) where the "p" value is the x-coordinate of the vertex and the "q" is the y-coordinate of the vertex.

Given the vertex (-2, 5) the "p" here is -2 and "q" here is 5, so plugging into the vertex form we get y=3(x+2)^2+5

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Notice that the alternative hypothesis is a two-tailed test. Suppose ttest_ind method from scipy module is used to perform the t

Korvikt [17]

Answer:

The p-value of the test is 0.0512.

Step-by-step explanation:

The p-value of a test is well-defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.

In this case the output of the t-test_ind method from scipy module is provided as follows:

Output = (-1.99, 0.0512)

The first value within the parentheses is the test statistic value.

So the test statistic value is, -1.99.

And the second value within the parentheses is the p-value of the test.

So the p-value of the test is 0.0512.

6 0

3 years ago

Start time 2:15 a.m elapsed time 45 minutes

Ronch [10]

Answer:

It would be 3:00 am.

Step-by-step explanation:

Start time is given = 2:15 a.m

elapsed time = 45 minutes

After 45 minutes of start time, time is = 02:15 + 00:45

= 03:00 am.

After 45 minutes elapsed time, the time would be 3:00 am.

5 0

3 years ago

Read 2 more answers

C. The double shadedregion represents of the whole.

Ede4ka [16]

Step-by-step explanation:

please the information needed is up the paper. you took a picture of no. 2 instead of no. 1

5 0

2 years ago

4. Find the solution for each equation: x + 4 = 16

Alex777 [14]

Answer:

$x=12$

Step-by-step explanation:

when solving and equation with a variable, you must work backwards and do the opposite of the equation

sooo… you must subtract 4 (opposite of +4 is -4)

$16-4=2$

x=12

3 0

2 years ago

Read 2 more answers

Can someone please help mee (20 points and i will give brainliest!!!)

FromTheMoon [43]

Answer:

a. y-intercept:(0, -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)

b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)

Step-by-step explanation:

So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes $y=(0)^2-0-6$ which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\$ . In this case a=1, b=-1, c=-6. So plugging those values in you get $x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)}$ , which simplifies to $x=\frac{1\pm5}{2}$ . This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of $y=(x-h)^2+k$ where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be

Move c to the other side

$y+6=x^2-x$

Complete the square by adding (b/2)^2

$y+6+0.25 = x^2-x+0.25$

Rewrite as square binomial

$y+6.25 = (x-0.5)^2$

Isolate y

$y=(x-0.50)^2-6.25$

(h, k) = 0.50, -6.25 which is the vertex

b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation $y=\frac{-(1)\pm\sqrt{1^2-4(-1)(6)}}{2(-1)}$ . which simplifies to $x=\frac{-1\pm5}{-2}$ which gives the values -2 and 3. To find the vertex it's the same process as before

Factor out -1

$y=-(x^2-x-6)$

Add 6 to both sides (on the left side add -6 since -1 was factored out).

$y-6=-(x^2-x)$

Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)

$y-6-0.25 = -(x^2-x+0.25)$

Rewrite as square binomial

$y-6.25=-(x-0.5)^2$

Add 6.25 to both sides

$y=(x-0.50)^2+6.25$

(h, k) = (0.50, 6.25)

When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.

4 0

2 years ago

Read 2 more answers