Evaluate a + 4 when a = 7

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

2 years ago

A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the students, Sandra,

nata0808 [166]

Answer:

What is P(A), the probability that the first student is a girl? (3/4)

What is P(A), the probability that the first student is a girl? (3/4)What is P(B), the probability that the second student is a girl? (3/4)

What is P(A), the probability that the first student is a girl? (3/4)What is P(B), the probability that the second student is a girl? (3/4)What is P(A and B), the probability that the first student is a girl and the second student is a girl? (1/2)

The probability that the first student is a girl is (3/4), likewise for the 2nd 3rd and 4th it's still (3/4). The order you pick them doesn't matter.

However, once you're looking at P(A and B) then you're fixing the first position and saying if the first student is a girl what's the probability of the second student being a girl.

3 0

3 years ago

Finding the percent of increase or decrease

madam [21]

What is the question

4 0

3 years ago

a rectangle has an area of 1/6 squar centimeters and a length of 1.5 centimeters what is the width and the perimeter

Alex73 [517]

(1/6)/ 1.5 =
(1/6)/(15/10)=
1/6*10/15=10/90=1/9 width

3 0

3 years ago

Answer quick find the coordinates

Mekhanik [1.2K]

Answer:

(-4, -3), (4, -1), (8, 0), (12, 1)

Step-by-step explanation:

The x- and corresponding y-values are listed in the table. Put each pair in parentheses, x-value first. (That is an ordered pair.)

(x, y) = (-4, -3) . . . . from the first table entry

(x, y) = (4, -1) . . . . from the second table entry

(x, y) = (8, 0) . . . . from the third table entry

(x, y) = (12, 1) . . . . from the last table entry

3 0

3 years ago