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

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Answer 1 · 2017-04-26T10:23:34

In vertex form we have:

$y=-1/25(x+18)^2+2$

We can use the vertex standardised form:

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

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

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

Also $k=color(red)(2)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So now we have:

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

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

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

$" "-7=225a+2$

$" "(-7-2)/225=a$

$" "a=-1/25$

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

Tony B

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