What is the equation of the parabola that has a vertex at $(- 18, 2)$ $(-18, 2)$ and passes through point $(- 3, - 7)$ $(-3,-7)$ ?

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Answer 1 · 2017-04-26T10:23:34

In vertex form we have:

$y = - \frac{1}{25} {(x + 18)}^{2} + 2$ $y=-1/25(x+18)^2+2$

We can use the vertex standardised form:

$y = a {(x + d)}^{2} + k$ $y=a(x+d)^2+k$

As the vertex $\to (x, y) = (- 18, 2)$ $->(x,y)=(color(green)(-18),color(red)(2))$

Then $(- 1) \times d = - 18 \Rightarrow d = + 18$ $(-1)xxd=color(green)(-18)" "=>" "d=+18$

Also $k = 2$ $k=color(red)(2)$
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So now we have:

$y = a {(x + d)}^{2} + k \to y = a {(x + 18)}^{2} + 2$ $y=a(x+d)^2+k" "->" "y=a(x+18)^2+2$

Using the given point of $(- 3, - 7)$ $(-3,-7)$ we substitute to determine $a$ $a$

$y = a {(x + 18)}^{2} + 2 \to - 7 = a {(- 3 + 18)}^{2} + 2$ $y=a(x+18)^2+2" "->" "-7=a(-3+18)^2+2$

$- 7 = 225 a + 2$ $" "-7=225a+2$

$\frac{- 7 - 2}{225} = a$ $" "(-7-2)/225=a$

$a = - \frac{1}{25}$ $" "a=-1/25$

Thus $y = a {(x + d)}^{2} + k \to y = - \frac{1}{25} {(x + 18)}^{2} + 2$ $y=a(x+d)^2+k" "->" "y=-1/25(x+18)^2+2$

Tony B

What is the equation of the parabola that has a vertex at (-18, 2) (−18,2) (-18, 2) and passes through point (-3,-7) (−3,−7) (-3,-7) ?