Solve -7x2 + 2 = -19 Oa +3 Ob +1.73 ос No Solution What is the answer

What is the standard form given the vertex (-3,3) and the focus point (-3,2)

baherus [9]

Answer:

$y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{3}{4}$

Step-by-step explanation:

The standard form of a parabola is written as

$y=ax^2+bx+c$

where a, b and c are the coefficients of the second-degree, first degree and zero-degree terms.

The coordinates of the vertex of a parabola is given by:

$x_b = -\frac{b}{2a}$

$y_b=c-\frac{b^2}{4a}$

The coordinates of the focus instead are given by

$x_f=-\frac{b}{2a}$

$y_f=y_b+\frac{1}{4a}$

In this problem, we know the coordinates of the vertex and of the focus point:

Vertex: (-3,3)

Focus point: (-3,2)

So we have:

$x_b=-3=-\frac{b}{2a}$ (1)

$y_b=3=c-\frac{b^2}{4a}$ (2)

$y_f=2=y_b+\frac{1}{4a}$ (3)

From eq.(1) we get

$2a=\frac{b}{3}$ (4)

Substituting into (2),

$3=c-\frac{b^2}{2(b/3)}\\3=c-\frac{3}{2}b\\c=3+\frac{3}{2}b$ (5)

Now rewriting eq.(3) as

$2=y_b+\frac{1}{4a}\\2=(c-\frac{3}{2}b)+\frac{1}{4a}$

And substituting (4) and (5) into this, we can find b:

$2=((3+\frac{3}{2}b)-\frac{3}{2}b)+\frac{1}{2(b/3)}\\2=3+\frac{3}{2b}\\-1=\frac{3}{2b}\\b=-\frac{3}{2}$

Then we can find a and c:

$2a=\frac{b}{3}\\a=\frac{b}{6}=\frac{-3/2}{6}=-\frac{1}{4}$

And

$c=3+\frac{3}{2}b=3+\frac{3}{2}(-\frac{3}{2})=3-\frac{9}{4}=\frac{3}{4}$

So the parabola is

$y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{3}{4}$

4 0

4 years ago

The product of 8 and four more than a number The algebraic expression is:

katovenus [111]

Answer:

8(n+4)

Step-by-step explanation:

4 0

3 years ago

Carry out the following operations, and express the answer with the appropriate number of significant figures:

inn [45]

I don't understand your question

6 0

4 years ago

The ratio of pencils to erasers is 4:1 if there are 20 pencils how many erasers are there? Kerion has a beaded necklace business

Misha Larkins [42]

Answer:

we express the ratio of pencil to eraser and multiply it by the number of the number of pencils and erasers. 4/5 * x=20 , so x=25, then it implies that there are 5 erasers.

7 0

4 years ago

Solve this please and thank you

natulia [17]

Answer:

x = 6 and DF = 3*6-3 = 15

Step-by-step explanation:

Given triangles are similar and their side lengths are proportional

the similarity ratio for this pair is 4/8 = 1/2

the length of DF:

(7.5)/(3x - 3) = 1/2 cross multiply expressions

3x - 3 = 15 add 3 to both sides

3x = 18 divide both sides by 2

x = 6 and DF = 3*6-3 = 15

4 0

3 years ago