Question
find the axis of symmetry of y=x^2-4x+19
Answers
GPT-4o mini
To find the axis of symmetry of the quadratic function \( y = ax^2 + bx + c \), we can use the formula:
\[
x = -\frac{b}{2a}
\]
In your equation, \( y = x^2 - 4x + 19 \), the coefficients are:
- \( a = 1 \)
- \( b = -4 \)
- \( c = 19 \)
Now, substitute the values of \( a \) and \( b \) into the formula:
\[
x = -\frac{-4}{2 \cdot 1} = \frac{4}{2} = 2
\]
Thus, the axis of symmetry for the function \( y = x^2 - 4x + 19 \) is \( x = 2 \).
\[
x = -\frac{b}{2a}
\]
In your equation, \( y = x^2 - 4x + 19 \), the coefficients are:
- \( a = 1 \)
- \( b = -4 \)
- \( c = 19 \)
Now, substitute the values of \( a \) and \( b \) into the formula:
\[
x = -\frac{-4}{2 \cdot 1} = \frac{4}{2} = 2
\]
Thus, the axis of symmetry for the function \( y = x^2 - 4x + 19 \) is \( x = 2 \).