Consider a quadratic function in $x$ $$y = ax^2 + bx + c$$ such that the graph of function (1) passes through the two points $(-1, -1)$ and $(2, 2)$. (1) When we express $b$ and $c$ in terms of $a$, we have $$b = \mathbf{A} - a, \quad c = \mathbf{BC}a.$$ (2) Suppose that one of the points of intersection of the graph of function (1) and the $x$-axis is within the interval $0 < x \leqq 1$. Then the range of values of $a$ is [see figure]. (3) When the value of $a$ varies within interval (2), the range of values of $a + bc$ is $$\frac{\mathbf{GH}}{\square\mathbf{I}} \leqq a + bc \leqq \square.$$
Consider a quadratic function in $x$
$$y = ax^2 + bx + c$$
such that the graph of function (1) passes through the two points $(-1, -1)$ and $(2, 2)$.
(1) When we express $b$ and $c$ in terms of $a$, we have
$$b = \mathbf{A} - a, \quad c = \mathbf{BC}a.$$
(2) Suppose that one of the points of intersection of the graph of function (1) and the $x$-axis is within the interval $0 < x \leqq 1$. Then the range of values of $a$ is [see figure].
(3) When the value of $a$ varies within interval (2), the range of values of $a + bc$ is
$$\frac{\mathbf{GH}}{\square\mathbf{I}} \leqq a + bc \leqq \square.$$