The incorrect inequality is g > 80. The symbol ">" means greater than. So g > 80 would translate to meaning Kyle's grandmother is greater than 80. However, the problem states that his grandmother is not more than 80, meaning she is either 80 or younger. So the inequality should be g ≤ 80, or Kyle's grandmother is less than or equal to 80 years of age.

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A parabola can be drawn given a focus of (-5, -4)(−5,−4) and a directrix of y=-6y=−6. Write the equation of the parabola in any

lord [1]

Answer:

$\displaystyle \large{y=\dfrac{x^2}{4} + \dfrac{5x}{2} + \dfrac{5}{4}}$

Step-by-step explanation:

Given:

Focus = (-5,-4)
Directrix = -6

To find:

Parabola Equation

Locus of Parabola (Upward/Downward)

$\displaystyle \large{\sqrt{(x-a)^2+(y-b)^2} = |y-c|}$

Where:

(a,b) = focus
c = directrix

Hence:

$\displaystyle \large{\sqrt{(x+5)^2+(y+4)^2}=|y+6|}$

Cancel square root by squaring both sides as we get:

$\displaystyle \large{(x+5)^2+(y+4)^2=(y+6)^2}$

Solve for y-term:

$\displaystyle \large{(x+5)^2=(y+6)^2-(y+4)^2}\\\displaystyle \large{x^2+10x+25=y^2+12y+36-y^2-8y-16}\\\displaystyle \large{x^2+10x+25=4y+20}\\\displaystyle \large{x^2+10x+5=4y}\\\displaystyle \large{y=\dfrac{x^2}{4} + \dfrac{5x}{2} + \dfrac{5}{4}}$