# How do you find the VERTEX of a parabola #f(x)= -x^2 + 3x + 10#?

Find vertex of

Vertex

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The vertex is

y = 9/4 + 9/2 * 2/2 + 10 * 4/4#

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To find the vertex of a parabola in the form ( f(x) = ax^2 + bx + c ), you can use the formula ( x = \frac{-b}{2a} ) to find the x-coordinate of the vertex, and then substitute this value into the equation to find the corresponding y-coordinate. For the given equation ( f(x) = -x^2 + 3x + 10 ), the x-coordinate of the vertex is ( x = \frac{-3}{2(-1)} = \frac{3}{2} ). Substituting ( x = \frac{3}{2} ) into the equation gives ( f\left(\frac{3}{2}\right) = -\left(\frac{3}{2}\right)^2 + 3\left(\frac{3}{2}\right) + 10 = \frac{7}{4} ). So, the vertex of the parabola is ( \left(\frac{3}{2}, \frac{7}{4}\right) ).

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