What is the equation of the parabola that has a vertex at $(- 8, 5)$ $(-8, 5)$ and passes through point $(2, 27)$ $(2,27)$ ?

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Answer 1 · 2016-03-20T07:04:08

${(x - - 8)}^{2} = + (\frac{50}{11}) (y - 5)$ $(x--8)^2=+(50/11)(y-5)" "$ Vertex Form

From the given: Vertex (-8, 5) and passing thru (2, 27), the parabola opens upward. The reason is that the vertex is lower than the given point.

By the vertex form , we can solve for the value of $p$ $p$

${(x - h)}^{2} = + 4 p (y - k)$ $(x-h)^2=+4p(y-k)$

${(2 - - 8)}^{2} = + 4 p (27 - 5)$ $(2--8)^2=+4p(27-5)$

$10^{2} = 4 p (22)$ $10^2=4p(22)$

$100 = 4 (22) p$ $100=4(22)p$

$25 = 22 p$ $25=22p$

$p = \frac{25}{22}$ $p=25/22$

Go back to the vertex form

${(x - - 8)}^{2} = + 4 (\frac{25}{22}) (y - 5)$ $(x--8)^2=+4(25/22)(y-5)$

${(x - - 8)}^{2} = + 2 (\frac{25}{11}) (y - 5)$ $(x--8)^2=+2(25/11)(y-5)$

${(x - - 8)}^{2} = + (\frac{50}{11}) (y - 5)$ $(x--8)^2=+(50/11)(y-5)" "$ Vertex Form

graph{(x--8)^2=(50/11)(y-5)[-50,50,-25,25]}

God bless....I hope the explanation is useful.

What is the equation of the parabola that has a vertex at (-8, 5) (−8,5) (-8, 5) and passes through point (2,27) (2,27) (2,27) ?