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Digital SAT
Digital SAT Mathematics - No Calculator Section

Finding the Y-Coordinate of a Quadratic Vertex

Very Hard Passport To Advanced Math Quadratic Equations

Consider the quadratic equation given by:

$$ax^2 + bx + c = 0$$

where $a$, $b$, and $c$ are real constants with $a eq 0$. The vertex of the parabola represented by this equation is given by the coordinates:

$$\left( -\frac{b}{2a}, -\frac{D}{4a} \right)$$

where $D$ is the discriminant, calculated as:

$$D = b^2 - 4ac$$

For this problem, assume that $a = 2$, $b = -12$, and $c = 22$. Calculate the $y$-coordinate of the vertex of the parabola represented by this quadratic equation, and express your answer as a decimal.

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