A quadratic function has vertex (0, -3) and passes through the point (10, -8). Which equation represents...

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A quadratic function has vertex (0, -3) and passes through the point (10, -8). Which equation represents the function?
f(x) = -\frac{1}{20}(x + 3)^2
f(x) = \frac{1}{20}(x + 3)^2
f(x) = -\frac{1}{20}x^2 - 3
f(x) = \frac{1}{20}x^2 - 3

SnapAndSolve AI · Accepted Answer

The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex. Here, the vertex is (0, -3), so the equation becomes f(x) = a(x - 0)^2 - 3 or f(x) = ax^2 - 3.

We need to find the value of 'a' using the point (10, -8):

Substitute x = 10 and f(x) = -8 into the equation: -8 = a(10)^2 - 3.
Simplify: -8 = 100a - 3.
Add 3 to both sides: -5 = 100a.
Divide by 100: a = -\frac{1}{20}.

The correct equation is f(x) = -\frac{1}{20}x^2 - 3.

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A quadratic function has vertex (0, -3) and passes through the point (10, -8). Which equation represents...

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