Determine the equation of a quadratic relation in vertex form. given the following information.
a) vertex at $(0, 3)$ , passes through $(2, - 5)$

Answer

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Answer

$y = - 2 x^{2} + 3$ is the equation of the quadratic relation in vertex form.

Steps

Step 1 ：Given the vertex form of a quadratic relation: $y = a (x - h)^{2} + k$ , where $(h, k)$ is the vertex of the parabola.

Step 2 ：Substitute the given vertex $(0, 3)$ into the equation: $y = a (x - 0)^{2} + 3$ or $y = a x^{2} + 3$ .

Step 3 ：Use the given point $(2, - 5)$ to find the value of $a$ : $- 5 = a (2^{2}) + 3$ .

Step 4 ：Solve for $a$ : $- 5 = 4 a + 3$ => $a = - 2$ .

Step 5 ：Substitute the value of $a$ back into the equation: $y = - 2 x^{2} + 3$ .

Step 6 ： $y = - 2 x^{2} + 3$ is the equation of the quadratic relation in vertex form.