Let $a$ and $b$ be constants where $a > 0$. Translate the graph of the quadratic function $$y = 4x^2 + 2ax + b$$ by $a$ in the $x$-direction and by $1 - 7a$ in the $y$-direction. If this graph passes through the point $(0, 4)$, we have $$b = \mathbf{AB}\, a^2 + \mathbf{C}\, a + \mathbf{D}$$ and the quadratic function representing the graph resulting from these translations is $$y = \mathbf{E}\, x^2 - \mathbf{F}\, ax + \mathbf{G}.$$ When the graph of quadratic function (1) is tangent to the $x$-axis, we have $a = \frac{\mathbf{H}}{\mathbf{I}}$, and the $x$-coordinate of the point of tangency is $x = \mathbf{J}$.
Let $a$ and $b$ be constants where $a > 0$. Translate the graph of the quadratic function
$$y = 4x^2 + 2ax + b$$
by $a$ in the $x$-direction and by $1 - 7a$ in the $y$-direction. If this graph passes through the point $(0, 4)$, we have
$$b = \mathbf{AB}\, a^2 + \mathbf{C}\, a + \mathbf{D}$$
and the quadratic function representing the graph resulting from these translations is
$$y = \mathbf{E}\, x^2 - \mathbf{F}\, ax + \mathbf{G}.$$
When the graph of quadratic function (1) is tangent to the $x$-axis, we have $a = \frac{\mathbf{H}}{\mathbf{I}}$, and the $x$-coordinate of the point of tangency is $x = \mathbf{J}$.