What is the equation of the parabola that has a vertex at $(2, -9)$ and passes through point $(12, -4)$ ?

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Answer 1 · 2018-06-10T10:11:13

$y=1/20(x-2)^2-9$ in Vertex Form of the equation

Given:
Vertex $->(x,y)=(2-9)$
Point on curve $->(x,y)=(12,-4)$

Using the completed square format of a quadratic

$y=a(x+b/(2a))^2+k$

$y=a(xcolor(red)(-2))^2color(blue)(-9)$

$x_("vertex")=(-1)xx(color(red)(-2)) = +2" "$ Given value
$y_("vertex")=color(blue)(-9)" "$ Given value

Substituting for the given point

$-4=a(12-2)^2-9$

$-4=a(100)-9$

$a=5/100=1/20$ giving:

$y=1/20(x-2)^2-9$ in Vertex Form of the equation

Tony B

What is the equation of the parabola that has a vertex at (2, -9) (2, -9) and passes through point (12, -4) (12, -4) ?