Mathematics: Part 3: Use the information provided to write the vertex formula of each parabola. Please show the work1. Vertex: (-4, -3), Directrix: y = -25/82. Vertex: (-8, -7), Directrix: y= -25/43. Focus: (7, 1/2), Directrix: y = 3/2

20 yearsStep-by-step explanation:A=500(1+.03)^20 $903A=100(1+.12)^20$964It took her 20 years to overtake....

Part 3: Use the information provided to write

Ответ:

miztati1280

23.01.2022

Mathematics

1. y = 2(x + 4)² - 3

$\bold{2.\quad y=-\dfrac{1}{3}(x+8)^2-7}$

$\bold{3.\quad y=-\dfrac{1}{2}(x-7)^2+1}$

Step-by-step explanation:

Notes: The vertex form of a parabola is y = a(x - h)² + k

(h, k) is the vertexp is the distance from the vertex to the focus

$\bullet\quad a=\dfrac{1}{4p}$

$\text{Vertex}=(-4,-3)\qquad \text{Directrix}:y=-\dfrac{25}{8}\\\\\text{Given}:(h, k)=(-4, 3)\\\\p=\dfrac{-24}{8}-\dfrac{-25}{8}=\dfrac{1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{8})}=\dfrac{1}{\frac{1}{2}}=2$

Now input a = 2 and (h, k) = (-4, -3) into the equation y = a(x - h)² + k

y = 2(x + 4)² - 3

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$\text{Vertex}=(-8,-7)\qquad \text{Directrix}:y=-\dfrac{-25}{4}\\\\\text{Given}:(h, k)=(-8, -7)\\\\p=\dfrac{-28}{4}-\dfrac{-25}{4}=\dfrac{-3}{4}}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-3}{4})}=\dfrac{1}{-3}=-\dfrac{1}{3}$