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Maksim231197 [3]
3 years ago
11

Write the equation of a parabola with a vertex at (0,0), a focus at (2,0), and directrix x=-2

Mathematics
1 answer:
kkurt [141]3 years ago
8 0
The directrix is x=-2, which means the parabola opens horizontally instead of vertically. The equation is (y - k)²<span> = 4p (x - h), where the </span>focus<span> is (h + p, k) and the </span>directrix<span> is x = h - p
in this case, h+p=2, k=0, and h-p=-2
solve for h and p: h=0, p=2
plug the numbers into the equation: (y-0)</span>²=4*2(x-0)
simplify: y²=8x
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Simplify. (x2+2x-4)+(2x-5x-3)​
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Answer:

Step by Step Solution

More Icon

STEP

1

:

3

Simplify ——

x2

Equation at the end of step

1

:

3

((((2•(x2))-5x)-——)+2x)-3

x2

STEP

2

:

Equation at the end of step

2

:

3

(((2x2 - 5x) - ——) + 2x) - 3

x2

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using x2 as the denominator :

2x2 - 5x (2x2 - 5x) • x2

2x2 - 5x = ———————— = ———————————————

1 x2

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

2x2 - 5x = x • (2x - 5)

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (2x-5) • x2 - (3) 2x4 - 5x3 - 3

————————————————————— = —————————————

x2 x2

Equation at the end of step

4

:

(2x4 - 5x3 - 3)

(——————————————— + 2x) - 3

x2

STEP

5

:

Rewriting the whole as an Equivalent Fraction :

5.1 Adding a whole to a fraction

Rewrite the whole as a fraction using x2 as the denominator :

2x 2x • x2

2x = —— = ———————

1 x2

Polynomial Roots Calculator :

5.2 Find roots (zeroes) of : F(x) = 2x4 - 5x3 - 3

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

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