Question

Write an equation of the parabola in intercept form that passes through 
(−18, 72) with x-intercepts of −16 and −2.

An equation of the parabola is y=

​

Answer 1

Answer:

y=9/4(x+16)(x+2)

Step-by-step explanation:

y=a(x-r)(x-s)

-16 & -2

y=a(x-(-16))(x-(-2))

y=a(x+16)(x+2)

Now we need to find a by plugging (-18, 72) into the equation.

72=a(-18+16)(-18+2)

72=a(-2)(-16)

72=a(32)

a=72/32

a=9/4

Finally, we get y=9/4(x+16)(x+2).

Answer 2

Equation of parabola is $\boldsymbol{\frac{16}{x}+\frac{2}{y}=-1}$

Equation of parabola in intercept form that passes through $(x,y)=(-18,-72)$ with $\boldsymbol{x}-$intercept of $(-16,0)=(p,0),(-2,0)=(q,0)$ is given as follows:

$\boldsymbol{y=a(x-p)(x-q)}$

$72=a(-18+16)(-18+2)$

$72=a(-2)(-16)$

 $a=\frac{72}{-2(-16)}$

    $=\frac{9}{4}$

$\boldsymbol{a=\frac{9}{4} }$

So,

$72=\frac{9}{4} (x+16)(y+2)$

$32=(x+16)(y+2)$

$32=xy+2x+16y+32$

 $0=xy+2x+16y$

Divide both sides of this equation by $\boldsymbol{xy}$

$0=1+\frac{2}{y} +\frac{16}{x}$

$\boldsymbol{\frac{16}{x}+\frac{2}{y}=-1}$

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