How do you find the equation for the parabola with the vertex (1,4) that passes through the point (3,8)?

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How do you find the equation for the parabola with the vertex (1,4) that passes through the point (3,8)?

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Answer 1 · 2018-06-12T06:16:19

$y = {(x - 1)}^{2} + 4$ $y=(x-1)^2+4$

Explanation:

Given -

Vertex $(1, 4)$ $(1, 4)$
Point $(3, 8)$ $(3, 8)$

The formula is

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

Where -

$h = 1$ $h=1$
$k = 4$ $k=4$

Then-

$y = a {(x - 1)}^{2} + 4$ $y=a(x-1)^2+4$

Find the value of $a$ $a$ when one of the points is $(3, 8)$ $(3, 8)$

$8 = a {(3 - 1)}^{2} + 4$ $8=a(3-1)^2+4$
$8 = 4 a + 4$ $8=4a+4$
$4 a + 4 = 8$ $4a+4=8$
$4 a = 8 - 4 = 4$ $4a=8-4=4$
$4 a = 4$ $4a=4$
$a = \frac{4}{4} = 1$ $a=4/4=1$
$a = 1$ $a=1$

$y = 1 {(x - 1)}^{2} + 4$ $y=1(x-1)^2+4$

$y = {(x - 1)}^{2} + 4$ $y=(x-1)^2+4$

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How do you find the equation for the parabola with the vertex (1,4) that passes through the point (3,8)?

1 Answer

Explanation:

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