What is the equation of the parabola that has a vertex at $(3, 3)$ $(3, 3)$ and passes through point $(13, 6)$ $(13, 6)$ ?

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Answer 1 · 2017-08-03T05:15:55

The equation is $y = \frac{3}{100} {(x - 3)}^{2} + 3$ $y=3/100(x-3)^2+3$

The equation of the parabola is

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

Where $(h, k)$ $(h,k)$ is the vertex

Therefore,

$h = 3$ $h=3$ and $k = 3$ $k=3$

So, the equation is

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

The parabola pases through the point $(13, 6)$ $(13,6)$

so,

$6 = a {(13 - 3)}^{2} + 3$ $6=a(13-3)^2+3$

$100 a = 3$ $100a=3$

$a = \frac{3}{100}$ $a=3/100$

The equation is

$y = \frac{3}{100} {(x - 3)}^{2} + 3$ $y=3/100(x-3)^2+3$

graph{y=3/100(x-3)^2+3 [-36.52, 36.54, -18.27, 18.28]}

What is the equation of the parabola that has a vertex at (3,3) (3, 3) and passes through point (13,6) (13, 6) ?