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Digital SAT
Digital SAT Mathematics - No Calculator Section

Finding Coefficient b from Vertex and Point

Medium Passport To Advanced Math Higher-order Equations

Consider the equation of a parabola given by the function:

$$f(x) = ax^2 + bx + c.$$

If the parabola has its vertex at the point (3, -2) and passes through the point (1, 2), determine the value of $b$ given that $a = 1$ and $c = -5$.

Recall that the x-coordinate of the vertex of a parabola described by the equation $$y = ax^2 + bx + c$$ is given by the formula $$x_v = -\f\frac{b}{2a}.$$ You will need to establish the relationship between $b$ and the given parameters.

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