Functions and graphs: แบบฝึกหัด

Determine whether the quadratic function \( y = -2x^2 + 5x - 1 \) has a maximum or minimum point, and state its nature.

The variables \( x \) and \( y \) satisfy the equation \( y = k \cdot 2^x \). Given that \( y = 3 \) when \( x = 0 \), find the value of \( y \) when \( x = 3 \).

The quadratic curve \( y = -x^2 + 4x + 12 \) intersects the \( x \)-axis at points \( A \) and \( B \), and has its maximum turning point at \( V \). Find the area of triangle \( ABV \).

State the coordinates of the turning point of the quadratic graph \( y = (x - 3)^2 + 5 \).

The graph of a quadratic function is given by \( y = -(x + 4)(x - 2) \). Find the coordinates of the points where the graph intersects the x-axis.

The graph of the quadratic function \( y = x^2 - 6x + k \) has a minimum value of \( -4 \). Find the value of the constant \( k \) and the coordinates of the minimum point.