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

$\boxed{y = -2x^2 + 3}$ 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 $y = ax^2 + 3$.

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

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

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

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