To determine the value of the constant term \( c \) in the standard form of a quadratic function \( y = ax^2 + bx + c \), we can utilize the information given about the graph of the quadratic function.
You've mentioned that the graph is "U shaped" and is "upwards on (1,-3)." This indicates that the vertex of the parabola is at the point \( (1, -3) \), which is also the minimum point of the function since the parabola opens upwards.
The vertex form of a quadratic function is given by:
\[ y = a(x - h)^2 + k \]
where \( (h, k) \) is the vertex of the parabola. Given that the vertex is \( (1, -3) \), we can substitute \( h = 1 \) and \( k = -3 \):
\[ y = a(x - 1)^2 - 3 \]
To convert this into standard form (which is \( y = ax^2 + bx + c \)), we expand it:
\[ y = a(x^2 - 2x + 1) - 3 \] \[ y = ax^2 - 2ax + a - 3 \]
From this expansion, we can observe that the constant term \( c \) in the equation \( y = ax^2 + bx + c \) is:
\[ c = a - 3 \]
However, to find the specific value of \( c \), we actually need the value of \( a \). If we consider that you haven’t provided additional points or conditions that allow us to determine \( a \), we can only express \( c \) in terms of \( a \):
\[ c = a - 3 \]
If you have any specific values for \( a \) or more information about the graph (such as another point on the graph), please provide that so we can calculate the exact value of \( c \). Otherwise, \( c \) generally depends on the value of \( a \).