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ella [17]
3 years ago
10

PLEASE HELP!!! I'LL GIVE YOU BRAINLIEST!

Mathematics
2 answers:
Andru [333]3 years ago
8 0
(x - a)^2 + (y - b)^2 = (y - d)^2 

<span>x^2 - 2ax + a^2 + y^2 - 2by + b^2 = y^2 - 2dy + d^2 </span>

<span>Subtract y^2 from both sides... </span>

<span>x^2 - 2ax + a^2 - 2by + b^2 = -2dy + d^2 </span>

<span>Now I would just substitute in the the values (a = -4, b = 17/8, d = 15/8)... </span>

<span>x^2 - 2(-4)x + (-4)^2 - 2(17/8)y + (17/8)^2 = -2(15/8)y + (15/8)^2 </span>

<span>Simplify... </span>

<span>x^2 + 8x + 16 - (17/4)y + 289/64 = -(15/4)y + 225/64 </span>

<span>Add (17/4)y to both sides... </span>

<span>x^2 + 8x + 16 + 289/64 = (2/4)y + 225/64 </span>

<span>x^2 + 8x + 16 + 289/64 = (1/2)y + 225/64 </span>

<span>Subtract 225/64 from both sides... </span>

<span>x^2 + 8x + 16 + 1 = (1/2)y </span>

<span>x^2 + 8x + 17 = (1/2)y </span>

<span>Multiply both sides by 2... </span>

<span>2x^2 + 16x + 34 = y </span>

<span>...which is equal to equation D.</span>
Andrew [12]3 years ago
4 0

Answer:

Option D - f(x)=2x^2+34+16x

Step-by-step explanation:

Given :  Focus F=(-4,\frac{17}{8}) and a directex  y=\frac{15}{8}

To find : What is the equation of the quadratic graph with a focus and directrix?

Solution :

The general form of the quadratic equation is  (x-h)^2=4p(y-k)

Where, Focus of the equation is  F=(h,k+p) and

Directrix is  y=k-p    

Comparing the given focus and directrix with the general one.

(-4,\frac{17}{8})=(h,k+p)

h=-4 and

k+p=\frac{17}{8} ....(1)

k-p=\frac{15}{8} .....(2)

Add equation (1) and (2)

2k=4

k=2

Substitute in equation (1)

2+p=\frac{17}{8}

p=\frac{17}{8}-2

p=\frac{17-16}{8}

p=\frac{1}{8}

Now, We get h=-4 , k=2 and p=\frac{1}{8}

Substitute in the general form,

(x-(-4))^2=4(\frac{1}{8})(y-2)

x^2+16+8x=\frac{1}{2}(y-2)

2x^2+32+16x=y-2

2x^2+32+16x=y-2

i.e, The equation of the quadratic graph is f(x)=2x^2+34+16x

Therefore, Option D is correct.

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