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

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

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Answer 1 · 2018-06-10T10:11:13

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

Explanation:

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

Using the completed square format of a quadratic

$y = a {(x + \frac{b}{2 a})}^{2} + k$ $y=a(x+b/(2a))^2+k$

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

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

Substituting for the given point

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

$- 4 = a (100) - 9$ $-4=a(100)-9$

$a = \frac{5}{100} = \frac{1}{20}$ $a=5/100=1/20$ giving:

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

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

1 Answer

Explanation:

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Science

Math

Humanities

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

1 Answer

Explanation:

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