How do you write the equation of the quadratic that has the vertex of (2,-3) and a point on (0,1)?

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How do you write the equation of the quadratic that has the vertex of (2,-3) and a point on (0,1)?

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Answer 1 · 2018-03-25T18:57:37

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

Explanation:

Vertex form of a quadratic equation: $y = a {(x - h)}^{2} + k$ $y=a(x-h)^2+k$ , where (h, k) represents the vertex

Plug in (2, -3) for (h, k).

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

$y = a {(x - 2)}^{2} - 3 \to$ $y=a(x-2)^2-3 rarr$ We still don't know what a is, so let's plug in the point (0, 1) to find what it is

$1 = a {(0 - 2)}^{2} - 3$ $1=a(0-2)^2-3$

$1 = a {(- 2)}^{2} - 3$ $1=a(-2)^2-3$

$1 = a (4) - 3$ $1=a(4)-3$

$1 = 4 a - 3$ $1=4a-3$

$4 a = 4$ $4a=4$

$a = 1$ $a=1$

Our equation would be $y = 1 {(x - 2)}^{2} - 3$ $y=1(x-2)^2-3$ once 1 is plugged in for a, but the 1 does not need to be written in the final answer because anything multiplied by 1 is itself

$y = {(x - 2)}^{2} - 3$ $y=(x-2)^2-3$ is the equation in vertex form

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How do you write the equation of the quadratic that has the vertex of (2,-3) and a point on (0,1)?

1 Answer

Explanation:

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