How do you write the vertex form of a parabola with (3,2.5) and (4,5.5)?

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Answer 1 · 2018-07-18T05:50:01

$y = 3 {(x - 3)}^{2} + 2.5$ $y=3(x-3)^2+2.5$

Let us take $(3, 2.5)$ $(3, 2.5)$ the vertex and passes through the point $(4, 5.5)$ $(4,5.5)$

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

Where -

$h = 3$ $h=3$
$k = 2.5$ $k=2.5$

Then -

$y = a {(x - 3)}^{2} + 2.5$ $y=a(x-3)^2+2.5$

To find the value of $k$ $k$ , assume the parabola is passing through the point $(4, 5.5)$ $(4, 5.5)$

Then -

$a {(4 - 3)}^{2} + 2.5 = 5.5$ $a(4-3)^2+2.5=5.5$

$a + 2.5 = 5.5$ $a+2.5=5.5$

$a = 5.5 - 2.5 = 3$ $a=5.5-2.5=3$

Plug in the value $a = 3$ $a=3$ in $y = a {(x - 3)}^{2} + 2.5$ $y=a(x-3)^2+2.5$

$y = 3 {(x - 3)}^{2} + 2.5$ $y=3(x-3)^2+2.5$

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