How do you write a quadratic equation with vertex; ( 2,-2 ); point: ( 4,10 )?

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How do you write a quadratic equation with vertex; ( 2,-2 ); point: ( 4,10 )?

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Answer 1 · 2017-06-10T00:39:17

The vertex form of a quadratic with vertex $(h, k)$ $(h,k)$ looks like this:

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

In this case, we already know $h = 2$ $h = 2$ and $k = - 2$ $k=-2$ , so our equation is:

$y = a {(x - 2)}^{2} - 2$ $y = a(x-2)^2-2$

So all we have to do is find $a$ $a$ . We can do this by plugging in the other point $(4, 10)$ $(color(red)4,color(blue)10)$ we were given (which we know works since it is on the parabola) and solving for $a$ $a$ .

$10 = a {(4 - 2)}^{2} - 2$ $color(blue)10 = a(color(red)4-2)^2-2$

$10 = a \cdot 2^{2} - 2$ $10 = a*2^2 - 2$

$10 = 4 a - 2$ $10 = 4a-2$

$12 = 4 a$ $12 = 4a$

$3 = a$ $3 = a$

Therefore, our equation is:

$y = 3 {(x - 2)}^{2} - 2$ $y = 3(x-2)^2-2$

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How do you write a quadratic equation with vertex; ( 2,-2 ); point: ( 4,10 )?

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