Question

If the graph is open downward will the a-value be negative or will it be negative because the data y intercept is negative

Answer 1

In a quadratic function represented by the equation \( y = ax^2 + bx + c \), the direction of the graph (whether it opens upward or downward) is determined by the value of the coefficient \( a \):

- If \( a > 0 \), the graph opens upward (forming a U-shape).
- If \( a < 0 \), the graph opens downward (forming an upside-down U-shape).

So, if the graph is opening downward, the \( a \)-value must be negative, regardless of the y-intercept or the values of \( b \) and \( c \).

The y-intercept (the value of \( c \) when \( x = 0 \)) can be positive, negative, or zero and does not affect the direction the parabola opens. It simply indicates the point at which the graph intersects the y-axis.