Find the distance between the points given. (-3,-4) and (0,0)

The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?

OleMash [197]

Answer:

The equation of the parabola is $y = -12\cdot x^{2}$ .

Step-by-step explanation:

Since the directrix is of the form $y = a$ , the parabola is vertical. The vertex of the parabola ( $V(x,y)$ ) is the midpoint between the focus ( $F(x,y)$ ) and a point of the directrix ( $P(x,y)$ ), that is to say:

$V(x,y) = \frac{1}{2}\cdot F(x,y) + \frac{1}{2}\cdot P(x,y)$ (1)

If we know that $F(x,y) = (0, -3)$ and $P(x,y) = (0, 3)$ , then the coordinates of the vertex of the parabola:

$V(x,y) = \frac{1}{2}\cdot (0, -3) + \frac{1}{2}\cdot (0, 3)$

$V(x,y) = (0, 0)$

The vertex factor ( $p$ ) is the distance of the focus with respect to the vertex:

$p = \sqrt{[F(x,y)-V(x,y)]\,\bullet \,[F(x,y)-V(x,y)]}$ (2)

If we know that $F(x,y) = (0, -3)$ and $V(x,y) = (0, 0)$ , then the vertex factor is:

$p = \sqrt{0^{2}+(-3)^{2}}$

$p = -3$

The equation of the parabola in the vertex form is described below:

$y - k = 4\cdot p \cdot (x-h)^{2}$ (3)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$h, k$ - Coordinates of the vertex.

If we know that $(h,k) = (0, 0)$ and $p = -3$ , then the equation of the parabola is $y = -12\cdot x^{2}$ .

6 0

3 years ago

Write (2x - 5)2 as a trinomial.

solniwko [45]

Answer:

$4x^2-20x+25$

Step-by-step explanation:

$(2x-5)^{2} \\(2x)^2+2(2x)(-5)+(-5)^2\\4x^2-20x+25$

7 0

4 years ago

Read 2 more answers

Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still oper

timama [110]

Binomial Problem with n = 50 and P(op) = 0.0.7

P(31<=50) = 1 - P(0<=x<=30) = 1 - binomcdf(50,0.7,30) = 1-0.0848 = 0.9152

5 0

3 years ago

An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an est

MrRa [10]

Answer:

85% level of the confidence interval is

(26.337, 26.662)

Step-by-step explanation:

Explanation:-

Given the size of the sample 'n' = 295

Mean of the sample x⁻ = 26.5

The Standard deviation of the Population = 2.7

85% level of the confidence interval is determined by

$(x^{-} - Z_{0.15} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.15} \frac{S.D}{\sqrt{n} })$

Critical value Z₀.₁₅ = 1.036

85% level of the confidence interval is determined by

$(x^{-} - Z_{0.15} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.15} \frac{S.D}{\sqrt{n} })$

$(26.9 -1.036 \frac{2.7}{\sqrt{295} } , 26.5 + 1.036 \frac{2.7}{\sqrt{295} })$

( 26.5 - 0.1628 , 26.5+0.1628)

(26.3372,26.6628)

7 0

3 years ago

The spinner at the right is divided into eight equal parts. Find the theoretical probability of

finlep [7]

Answer:

$\frac{3}{4}$ probability of landing on a number greater than 2 on the spinner.

Step-by-step explanation:

A theoretical probability is given by the number of desired outcomes divided by the number of total outcomes.

In this question:

8 possible outcomes(all numbers from 1 to 8).

6 desired outcomes(3, 4, 5, 6, 7 and 8, that is, all the numbers greater than 2). So

$p = \frac{6}{8} = \frac{3}{4}$

$\frac{3}{4}$ probability of landing on a number greater than 2 on the spinner.

4 0

3 years ago