Question
The value of c in the standard form of the quadratic function y equals ax squared plus BX + c is the graph has a parable at negative 2, -6
Answers
GPT-4o mini
To find the value of \( c \) in the standard form of a quadratic function \( y = ax^2 + bx + c \) given a point on the parabola, we can use the information provided.
The point given is \((-2, -6)\). This means when \( x = -2 \), \( y = -6 \).
We can substitute these values into the quadratic function:
\[
-6 = a(-2)^2 + b(-2) + c
\]
This simplifies to:
\[
-6 = 4a - 2b + c
\]
To find the exact value of \( c \), we would need additional information about the values of \( a \) and \( b \). However, if you only want to express \( c \) in terms of \( a \) and \( b \), we can rearrange the equation:
\[
c = -6 - 4a + 2b
\]
So, without more information about the coefficients \( a \) and \( b \), we cannot find a specific numerical value for \( c \). However, the expression above shows how \( c \) relates to \( a \) and \( b \). If you have any additional information about the parabola, such as its vertex, direction (whether it opens upwards or downwards), or another point on the graph, please provide that for a more definitive solution.
The point given is \((-2, -6)\). This means when \( x = -2 \), \( y = -6 \).
We can substitute these values into the quadratic function:
\[
-6 = a(-2)^2 + b(-2) + c
\]
This simplifies to:
\[
-6 = 4a - 2b + c
\]
To find the exact value of \( c \), we would need additional information about the values of \( a \) and \( b \). However, if you only want to express \( c \) in terms of \( a \) and \( b \), we can rearrange the equation:
\[
c = -6 - 4a + 2b
\]
So, without more information about the coefficients \( a \) and \( b \), we cannot find a specific numerical value for \( c \). However, the expression above shows how \( c \) relates to \( a \) and \( b \). If you have any additional information about the parabola, such as its vertex, direction (whether it opens upwards or downwards), or another point on the graph, please provide that for a more definitive solution.