https://file.aiquickdraw.com/mathbot/file/17274499810359kwac6ub.jpg

Based on the image, the graph is a parabola with a vertex at (4, 3) and another point at (5, 1). The quadratic function can be written in vertex form:

\[
g(x) = a(x - h)^2 + k
\]

where \((h, k)\) is the vertex. Here, \(h = 4\) and \(k = 3\), so:

\[
g(x) = a(x - 4)^2 + 3
\]

To find \(a\), use the point \((5, 1)\) that lies on the curve:

\[
1 = a(5 - 4)^2 + 3
\]

Simplifying:

\[
1 = a(1)^2 + 3
\]
\[
1 = a + 3
\]
\[
a = -2
\]

Thus, the equation of the quadratic function is:

\[
g(x) = -2(x - 4)^2 + 3
\]

Find the equation of the quadratic function g whose graph is shown below.

Solve for the equation of a quadratic function by using the vertex (4, 3) and another point (5, 1) on the graph. This step-by-step solution explains how to use the vertex form of a quadratic equation to find the function.

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