Evaluate the expression. 2 • 15

What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1? PLs HELP!!

Delicious77 [7]

ANSWER
$f(x)= \frac{1}{4} {(x - 1)}^{2}$

EXPLANATION

Since the directrix is
$y = - 1$

the axis of symmetry of the parabola is parallel to the y-axis.

Again, the focus being,

$(1,1)$

also means that the parabola will open upwards.

The equation of parabola with such properties is given by,

${(x - h)}^{2} = 4p(y - k)$
where
$(h,k)$

is the vertex of the parabola.

The directrix and the axis of symmetry of the parabola will intersect at
$(1, - 1)$

The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.

This implies that,
$h = \frac{1 + 1}{2} = 1$

and
$k = \frac{ - 1 + 1}{2} = 0$

The equation of the parabola now becomes,

$(x - 1) ^{2} = 4p(y - 0)$

$|p| = 1$

Thus, the distance between the vertex and the directrix.

This means that,

$p = - 1 \: or \: 1$

Since the parabola opens up, we choose
$p = 1$
Our equation now becomes,

${(x - 1)}^{2} = 4(1)(y - 0)$

This simplifies to
${(x - 1)}^{2} = 4y$

or

$y = \frac{1}{4} {(x - 1)}^{2}$

This is the same as,

$f(x)= \frac{1}{4} {(x - 1)}^{2}$

The correct answer is D .

4 0

2 years ago

WILL GIVE BRAINLIEST! PLS HELP!!!

velikii [3]

Answer: 140m

Step-by-step explanation:

8 0

2 years ago

What should be the b-value in the equation shown below if the equation is a perfect square trinomial?

masha68 [24]

Answer:

B=10

Step-by-step explanation:

It's a perfect square of equation ax²+2abx+b²

I'm the given equation a is 1 and b is 5 so 2(a)(b)=2(1)(5)=10

(ps: when I say b in the explanation I mean another b not the one in question as to not be confused)

4 0

1 year ago

What is undefined <br> I need help I don't understand this question

timurjin [86]

(4/9-9) and (4/0) are undefined as you can not divide by the value of 0.

4 0

2 years ago

A gas has weight of 5 pounds and a volume of 100 cubic feet. what's the specific volume of this gas

Leya [2.2K]

In thermodynamics, specific volume is considered to be an intrinsic property of matter. What we meant by intrinsic property is that, the value of this property does not change no matter the size of the sample. This is opposite to weight or volume which changes depending on the size of the sample.

By mathematical definition, specific volume is the ratio of the substance’s volume to its mass. Or in other words, this is the reciprocal of density.

The formula for density is:

density = mass / volume

Since specific volume is reciprocal so:

Specific volume = 1 / density = volume / mass

Calculating:

Specific volume = 100 ft^3 / 5 pounds

Specific volume = 20 ft^3 / pound

Or when asked in units of m^3 / kg, we convert:

Specific volume = (20 ft^3 / pound) (2.2 pound / kg) (1 m^3 / 35.3147 ft^3)

Specific volume = 1.246 m^3 / kg

3 0

2 years ago

Evaluate the expression. 2 • 15 – 7 + 4