Question

20 points Write the equation of parabola that has vertex (9,7) and passes through point (3,8).

Answer 1

Answer:

$y=\frac{1}{36}\left(x-9\right)^2+7$ is the the equation of parabola that has vertex (9,7) and passes through point (3,8).

Step-by-step explanation:

To solve this you need to use the vertex form of the equation of a parabola which is

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

Where (h, k)  are the coordinates of the vertex.

So, h = 9  and k =7

And one set of points on the graph

x = 3, y = 8

Solving the formula for $a$.

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

$8=a\left(3-9\right)^2+7$

$\mathrm{Switch\:sides}$

$a\left(3-9\right)^2+7=8$

$36a+7=8$

$36a=1$

$a=\frac{1}{36}$

To create a general formula for the parabola you would put in the values for a, h, and k and then simplify.

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

$y=\frac{1}{36}\left(x-9\right)^2+7$

Therefore, $y=\frac{1}{36}\left(x-9\right)^2+7$ is the the equation of parabola that has vertex (9,7) and passes through point (3,8).

The graph is also attached.

Keywords: equation of parabola, vertex, graph

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